Can My Religious Parents Legally Throw My Belongings Out If I Pay Them Rent Monthly?

hey everyone, first off, heres my location: California. I'm not really good with words, but i have a serious issue. as of today not even an hour ago, my parents sat me down in the living room and said the following: (worded as best as i can from memory)

"we have many friends who can see into the spirit realm, and every single one of them has told us the house is a safe and peaceful place but theres a corner where darkness is settling. (my room) we want all the "alphabet mafia" (lgbtq) stuff out by wednesday. we are going to go through your room that day and take everything that offends god out. that includes you getting rid of two of your reptiles for space."

important things to note: i am a lesbian. i have a girlfriend, a lesbian flag, a lesbian themed furry tail, and pride shirts. and my parents know this. i have six animals that ive had for YEARS since i was around seven years old. (my newest reptile, a painted agama being in my care for about a year and a half) i am nineteen now, turning twenty this year in july.
ive been paying my parents rent ($500 a month) since i was 17, almost 18.

i really feel like they shouldnt be able to just throw out things that dont fit well with their religion. i am a costume maker/fursuit maker, so i make furry heads, costumes, paws, cool gadgets, etc for people to make money as a side gig. lots of these items i have can range from ten bucks, to hundreds of dollars. can they legally throw these things out?? i plan on giving a box of all my lgbtq items to my friend for safe keeping, but i dont know what to do about the rest. i mean, ive lived in this house all my life, put up with their homophobic behavior, but now it feels like theyre doing this to me just for being me because apparently its "offending god". i feel this is utter bs and is just another way to try and control me and my sexuality.

i can answer any questions in the comments, and clear anything i may have worded strangely