My parents are making me (21F) pick between them or my boyfriend (23M)

Hi Reddit, I (21F) really need some outside perspective.
My parents absolutely hate my boyfriend (23M). He’s my very first boyfriend, we have been dating 9 months so far and they’ve been extremely strict about our relationship. Without getting into every detail, their main issues are his criminal record from a few years ago and an argument he had with my dad that almost got physical.
For context: my boyfriend has been on a good path these past two years. He’s clean of bad habits, hasn’t gotten into trouble, and he treats me really well and has a clear path on moving up in life. But my parents refuse to see his progress and are convinced he will fall back into his “bad past” and “drag me down with him.”
They’ve given me an ultimatum:
Move out and live with him at his mom’s house, or
Break up with him and stay living at home.

Here’s where it gets complicated. I have a 1-year-old cat and a bird I’ve had since I was 9. Getting my own place right now isn’t possible since I’m about to start college, just got a new job, and don’t have the funds yet because I need to save for a new car.
I haven’t spoken directly to my boyfriend’s mom yet, but I know she probably wouldn’t be okay with me bringing a bird (she’s very OCD and had issues with a previous roommate’s pets which led to the roommate being kicked out).
On top of that, she already has two herding dogs that don’t get along with cats, so I’d constantly be stressed about keeping them separated and keeping my cat safe—plus my cat would already be stressed leaving the two cats she currently lives with at my parents’ house.
My parents made it clear: if I choose him, they’ll cut me off completely and I will have no relationship with my family. They said they’ll change the locks, and I won’t be allowed to leave my pets behind because they “won’t be mine” anymore. Neither me or my boyfriend will be allowed on their property, so I can’t even just visit my pets.
I feel so stuck. I feel like either choice I make is not going to make me happy and I feel so pushed into a corner. I love my boyfriend, but I don’t want to lose my pets or my family either.
Has anyone been in a similar situation? What should I do?
TL;DR: My parents hate my boyfriend because of his past and gave me an ultimatum: move in with him and be cut off from my family (and lose my pets), or break up with him and stay at home. I love him, but I don’t want to lose my pets or my family. I feel completely stuck.