She almost definitely does NOT mean homosexuals. By pervert, she PROBABLY means someone who wants only sex. That is, she wants to meet someone who is interested in friendship or courtship, but not just sex.
But she could also mean someone who has other uncommon sexual interests. It's not clear really, because "perversion" means different things to different people.
"pervert", "psycho", "freak", "groupie", "geek", "insane"
Pervert is always sexual. So it means strange sexual interests.
Psycho means someone who is crazy.
Freak usually means weird, and is an insult. But, less commonly, it can also mean someone who does interesting sexual things, in which case it's not an insult.
A groupie is a woman or girl who loves a particular celebrity or band (music group). She might follow them around want to join their parties. She might offer sexual things, but she might not.
A geek can mean someone who doesn't know how to act socially (an insult). But when it's combined with another word, it can also mean anyone who is very interested in a topic. "A movie geek" is someone who knows a lot about movies and loves movies.
Insane means crazy.