My theory is that everybody thinks the platform they use is the best and most aligned with their politics because they've trained the algorithm to feed them the content they like.
YouTube hasn't shown me anything remotely right wing in ages, but every time I try tiktok I have to thumbs down 10 different channels that repost Joe Rogan and Elon musk clips.
If I was in your situation I would lie and say I didn't have a pet, sign the lease and smuggle them in. Put their crates inside cardboard boxes to carry them in. Then after a few weeks approach management and try to get permission to bring your emotional support cats in.
Worse case scenario you've bought yourself some time to save up to find a better place. Just make sure that if they find out to start looking for a place as soon as they give you notice to move because it's super hard to find an apartment with an open eviction case. Look into your state's laws, most states they require longer notice periods when the eviction isn't for non-payment of rent.
Normally I'd say be honest from the start so you can find a landlord that will accept them, but it seems like you're in a tough situation right now.