There is some severe issues with you not trusting those you work with. If you can't trust the people you're charging into burning building with, maybe try a lateral transfer. Or if you really want to change careers, maybe it's time. You honestly sound miserable at your station
I am so glad I am as fortunate as I am to live in the community I live in and volunteer with the station I'm with. We have plenty of firefighters here, men and women, who both accept and encourage anyone who comes to the station. We all go out together, we work well together, we joke. When one is struggling, everyone is there to lend a helping hand. Maybe I live in Firefighter Dreamland but as a female who happens to be a firefighter, I've encountered maybe three men out of all of them, who either blatantly or subtly suggested I can't keep up. You can't win them all. I've honestly encountered more absurd behavior from women, who insist the only reason to join a station is to find a hot firefighter husband -_- Suggest a night out after a shift change, invite a few outside friends to go (just in case they all say no) and invite THEM to YOUR outing. Maybe just breaking the ice is all you need.