Your history of tenancy isn't relevant, the only issue is whether your feeding of stray cats and your rescue activities is grounds for eviction. If you're in N. Hollywood, and your building is otherwise eligible, then it's under the Los Angeles rent stabliization ordinance, which means you can only be evicted for 12 specific things. One of these things is "nuisance," and your landlord, and a judge, may consider your cat rescue activities a nuisance.
Animal rescue activities are not something that's naturally part of your tenancy and not something you're able to do if it's disturbing anyone. Fighting an eviction may involve getting declarations from your fellow residents and other neighbors stating that this activity doesn't bother them, taking photos of the activity and the cats, etc. etc., and you may need or want to hire a lawyer. It's pretty hard to evict someone under LA rent control for reasons other than non-payment of rent, but this may provide a reason, if the landlord alleges and proves that residents or neighbors have complained about the cats, that the cats create noise, disease, threats to other animals and people, etc. etc.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.