Well fed cats who also sometimes go 'out' are not a serious threat to birds. They are opportunists whose instincts might do in an occasional careless bird, but they aren't normally out there hunting.

Now, in a situation where there are large numbers of feral cats, I'd not want to build a nest....but that's not very common in urban areas.

As we see, there are some serious differences of opinion about supposed 'studies'....my suspicion is that there is a large amount of emotional layering in this issue, both among cat fanciers AND among bird lovers.

(We had cats for years, mostly ones who went out....and VERY seldom had one actually get a bird.)