After researching this question, it seems to me that the mummy was afraid of cats in the 1999 movie because this was a popular plot element in previous mummy movies. Similarly, vampires are afraid of crosses and garlic in most vampire movies because it was a medieval myth. Not because there is any "reason" for it. The difference with the mummy vs. cat connection is that this seems primarily invented by movie producers who got it from the idea that cats were "guardians of the dead" in Egyptian mythology. There were other denizens of the underworld in Egyptian mythology that it would have made more sense for the mummies to be afraid of. For example in the original mummy movie with Boris Karlof, a cat is protecting the mummy and the mummy is afraid of Isis. That was more logical. However cats are cute and it was certainly brilliant to make mummies afraid of them in movies. I love the idea myself. I always wondered why in the movies the potential victims did not walk around with a half dozen cats in cat carriers. But then perhaps the plot could not progress as swiftly. Enough said.
I am looking for a list of movies with mummies afraid of cats. Evidently there were not as many as I seem to remember. I took it for granted the mummies were afraid of cats. However it seems that not many of my friends got the same impression from classical mummy movies. Perhaps some of what I remember was from television episodes. All I can say is that whoever wrote the 1999 mummy film must have seen the same films that I saw.