Cats were sacred animals (not gods) and they were treated with care and respect by all members of Egyptian society, being mourned as one would a family member when they died. A recorded penalty for killing a cat was death by the 4th Century BCE at least and the Roman historian and geographer Diodorus Siculus would recount witnessing the consequences of a Roman diplomat accidentally killing a cat in the 1st Century BCE:
And whoever intentionally kills one of these animals is put to death, unless it be a cat or an ibis that he kills; but if he kills one of these, whether intentionally or unintentionally, he is certainly put to death, for the common people gather in crowds and deal with the perpetrator most cruelly, sometimes doing this without waiting for a trial. And because of their fear of such a punishment any who have caught sight of one of these animals lying dead withdraw to a great distance and shout with lamentations and protestations that they found the animal already dead. 8 So deeply implanted also in the hearts of the common people is their superstitious regard for these animals and so unalterable are the emotions cherished by every man regarding the honour due to them that once, at the time when Ptolemy their king had not as yet been given by the Romans the appellation of “friend” and the people were exercising all zeal in courting the favour of the embassy from Italy which was then visiting Egypt and, in their fear, were intent upon giving no cause for complaint or war, when one of the Romans killed a cat and the multitude rushed in a crowd to his house, neither the officials sent by the king to beg the man off nor the fear of Rome which all the people felt were enough to save the man from punishment, even though his act had been an accident. And this incident we relate, not from hearsay, but we saw it with our own eyes on the occasion of the visit we made to Egypt.

But if what has been said seems to many incredible and like a fanciful tale, what is to follow will appear far more extraordinary. Once, they say, when the inhabitants of Egypt were being hard pressed by a famine, many in their need laid hands upon their fellows, yet not a single man was even accused of having partaken of the sacred animals.
This dramatic account was intended to underline the importance of cats in Egypt, however we know that sacred animals were killed in order to meet the sheer numbers of animals required to allow people to participate in the funerary and religious rites associated with the more popular animal cults. These popular cults also became favourite tourist destinations for Greek and Roman travellers who wished to view and experience the adorned sacred animals and witness the mummified animals. This extended from cats, to bulls, ibises and even crocodiles. Indeed, the killing of sacred animals in order to accommodate individuals desires to participate in sacred rites and gain the divine favour that followed is evidenced on a massive scale as is the pan-Mediterranean fascination with Egyptian cultic motifs.

The Egyptian reverence of cats was seen as peculiar by other contemporary Mediterranean civilisations, although the majority of my sources are Greek and Roman, but they were only one of several sacred animals the Egyptians held in high regard. Ibises are the other animals which received similar treatment to cats, these being associated with Thoth while cats were associated with Bastet, but crocodiles, cows, dogs, and hawks were also very important in certain regions. The various animal cults of Egypt were quite famous in Antiquity with the worship of sacred bulls and crocodiles being just as famous, if not more so, than the reverence of cats. Greek and Roman authors did most certainly demonstrate a degree of disdain for what they saw as a primitive and barbaric tradition. For this reason, and because of the animal cults’ localised nature, the anthropomorphised Egyptian deities were the only Egyptian cults to gain traction in the Hellenistic and Roman Mediterranea, while Egypt’s sacred animals were relegated to the status of exotic curiosities. There are records of Roman senators who visited Ptolemaic Egypt and went to feed the sacred and adorned crocodiles , as well as art depicting cats inna variety of sacred contexts being exported throughout the Mediterranean but these were not demonstrations of any pious devotion, rather they were signs of a growing interest in the exotic mysteries of Egypt, comparable to modern consumption of once religiously charged symbols and artefacts.

The 5th Century BCE account by the Greek historian Herodotus goes into detail on the Egyptian customs and laws concerning cats among other sacred animals but this is yet again within an account which emphasises Egypt’s unique attributes
Not only is the climate different from that of the rest of the world, and the rivers unlike any other rivers, but the people also, in most of their manners and customs, exactly reverse the common practice of mankind.

All other men pass their lives separate from animals, the Egyptians have animals always living with them;
He makes mention of Egyptian attitudes towards several animals hw considers noteworthy either for their peculiarity or because he believes they were the origin of Greek practces. This includes the veneration of heifers as Io/Hathor, the veneration of goats in certain animal cults which he associates with Pan, and the Egyptian aversion to pigs. When he lists specifically sacred animals he does emphasise cats and ibises, although he also mentions crocodiles, hawks, dogs, snakes and other animals being attached to cults in certain regions.
Egypt, though it borders upon Libya, is not a region abounding in wild animals. The animals that do exist in the country, whether domesticated or otherwise, are all regarded as sacred. If I were to explain why they are consecrated to the several gods, I should be led to speak of religious matters, which I particularly shrink from mentioning; the points whereon I have touched slightly hitherto have all been introduced from sheer necessity. Their custom with respect to animals is as follows:- For every kind there are appointed certain guardians, some male, some female, whose business it is to look after them; and this honour is made to descend from father to son. The inhabitants of the various cities, when they have made a vow to any god, pay it to his animals in the way which I will now explain. At the time of making the vow they shave the head of the child, cutting off all the hair, or else half, or sometimes a third part, which they then weigh in a balance against a sum of silver; and whatever sum the hair weighs is presented to the guardian of the animals, who thereupon cuts up some fish, and gives it to them for food- such being the stuff whereon they are fed. When a man has killed one of the sacred animals, if he did it with malice prepense, he is punished with death; if unwittingly, he has to pay such a fine as the priests choose to impose. When an ibis, however, or a hawk is killed, whether it was done by accident or on purpose, the man must needs die.

If a cat dies in a private house by a natural death, all the inmates of the house shave their eyebrows; on the death of a dog they shave the head and the whole of the body. The cats on their decease are taken to the city of Bubastis, where they are embalmed, after which they are buried in certain sacred repositories. The dogs are interred in the cities to which they belong, also in sacred burial-places. The same practice obtains with respect to the ichneumons; the hawks and shrew-mice, on the contrary, are conveyed to the city of Buto for burial, and the ibises to Hermopolis. The bears, which are scarce in Egypt, and the wolves, which are not much bigger than foxes, they bury wherever they happen to find them lying.
In all of these sources, from the Classical Greek to the Roman, the Egyptian attachment to cats is remarked upon but it is seen more as a facet of their excessive religiousness and superstition than a standalone point of interest. At the same time that it is conveyed as a strange custom it is not directly mocked by any sources I know of, excluding more general condescending attitudes towards Egyptian cults. Part of this may be attributable to the fact that while cats are one of the most commonplace and culturally significant pets around the world today, they were never nearly as popular in Greece or Rome. That said, there is evidence of domestic cats in Cyprus going back to a little less than 10,000 BCE, and cats appear in Greek literature and mythology with surprising frequency, and Aristophanes regularly referred to them in his works indicating that they would have been fairly well known as pets. Roman frescoes depict domestic cats exist dating to the early Principate along with archaeological evidence that they were fairly well distributed throughout the Roman Empire but they were never anywhere near as popular as dogs, birds and weasels. Within Graeco-Roman Egypt they were most popular, and they appear as pets in art and funerary epitaphs belonging to Roman individuals along with the more common dog. In all, cats were simply nowhere near as popular outside of Egypt as pets, although they were known to Phoenicians, Greeks, Persians and Romans, dogs were generally of a more practical value in the eyes of Graeci-Roman pet owners and were also held in higher esteem as a result but even this was nowhere near the devotion with which Egyptians viewed those sacred animals which were vessels of the divine and favourites of the gods.
Persian attitudes towards Egyptian cults as recounted by Greek histories imdicate that they were no more respected by Achaemenid contemporaries than their Greek counterparts. One example would perhaps be in the highly questionable anecdote surrounding the Egyptian’s humiliation at the hands of Cambyses II at the siege of Pelousion where the Persians forced the Egyptians to flee and surrender by driving sacred animals (mostly cats) before their army, holding cats and painting images of Bastet on their shields. Afterwards they apparently threw cats at…their faces. Needless to say, take this snippet from Polyaenus very lightly because no other source mentions it, however many of the Greek sources do claim that the Persians tyrannical rule of Egypt was typified by their contempt for Egyptian traditions which extended to their foreign cultic practices. Now the Greeks did love to villainise Persians and their accounts of Persian activity in Egypt is undeniably slanted but it is fair to say that they felt no more beholden to Egyptian superstition than anyone else.

In fact, the feline cults and veneration of cats in antiquity was more or less restricted to Africa where leonine deities represent some of the most primitive representations of gods and were the precursors to domestic cat deities like Bastet. Many deities like Hecate, Liberalia, and Artemis were sometimes associated with cats and even more were associated with lions such as Ishtar, Nergal, Shamash, and the ever popular Dionysius who was associated with the panther. Felines were therefore well known to have played a role in divine dramas and were often imbued with otherworldly qualities, either in their original creation or in their role as protectors or entities on the boundary of life and death but this was not always a good thing, their association with Hecate earned them a negative role in Greek mythology and an association with negative magic for instance, and the real world domestic cats were not afforded the same respect as their mythological counterparts in cultures where the line between deities in animal guise and animals was more distinguished.

In short, other cultures did not think much of Egyptian attitudes towards cats because a lot of Egypt’s neighbours thought they were pretty odd, wise and ancient, but odd. Cats were known as pets in the Mediterranean for millenia but Egypt was where they were most common and generally speaking where they were most liked so although the Egyptian reverence for cats is striking to us thanks to the significance of our relationship to cats, it was probably not more important to ancient peoples than any of Egypt’s other strange attitudes towards animals. When Greek and Roman individuals expressed interest in cats role in Egyptian spirituality (as pets, in art etc) it was usually with the a similar kind of curiousity that is within your question, because the idea of sacred animals and animal cults in general was sneered at by most Greek and especially Roman authors. Actually if anything, outside sources exaggerated Egyptian dedication to cats to a small extent but this holds true for many other facets of Egyptian culture.