Some blamed the Black Plague on Europeans who the thought cats were connected to witches and the Devil and killed them. That allowed rats to flourish and the fleas they carried spread the Plague.
That is an anti catholic lie repeated by those who should know better. The few reports of cat killing were sporadic, not general, and do not fit the time line.
The plague epidemic was also killing a lot of folks in Muslim lands, Hindu India and in China.
The main witch craze was after the reformation so could not have caused the black death to spread 200 years earlier.
Finally, Rats are also hunted by barnowls, snakes and dogs.
They thrive in garbage, and medieval cities were like third world cities today, but worse because of horse manure was there too.
I have heard that bandied about for years, I’m 67. But cats have fleas too sometimes and they are all over everything you own if you let them in your house. So fewer cats may mean more rats, but I don’t see lack of cats adding to the epidemic. The cleanliness and hygiene sucked back then. I keep my 3 for mouse control and fortunately where I live now there aren’t many four legged rats. I have seen rats the size of some cats. A good bullet works on them and on the two legged kind too.