My [21F] parents [50s] don't want me to have a lock on my door.

I'm graduating from college soon which means I might be moving home. My parents are currently house hunting, so I mentioned that if I was going to move home, I'd like to have a lock on my bedroom door.

Dad said no.

I told him that I was an adult that needed privacy and that this was a pretty normal request for someone to have. He literally said "What do you need privacy for? If the door is closed, we don't come in." Except they do, frequently. He gave more excuses, like "What if there's a fire?" but I'm not buying it. I even asked why he and mom didn't have a lock, because they're married, and he said "We don't need it." So I said, "I'm so sorry."

What if someone breaks into the house? I'm probably the most vulnerable, along with my sister (13F). I sometimes like sleeping nude in the summer, and also, surprise, I masturbate on occasion. (I can't just say that though because I may get kicked out. My dad is really religious.) And sometimes I just want alone time! Why is this such a big deal?

tl;dr: I might be moving home, told my parents I want a lock on my door, Dad said no way. What gives? What do I do? (Besides find a job and move somewhere else, which I'm already trying my best to do).