I am not saying you are right or wrong, it really could go either way.

But a key skill in IT is separating perception from fact. Your perception is sexism but do you have any facts to back it up? Does the perception of sexism come from anything other than the fact that they are men and you are a woman? Are your coworkers making comments like, "Here let me do it, this is man's work" or hitting on you or things like that?

Based on the info you have provided, these are all possibilities:

• They don't trust you because they are sexist
• They don't trust you because they are racist or anti-gay or they hate fat people or they hate skinny people or [insert applicable form of discrimination here]
• They don't trust you because you have no formal education in the industry (Comp. Science degree, certs, etc.)
• They don't trust you because you have lied to them in the past
• They don't trust you because you have failed in the past (remember that 1 failure undoes an entire lifetime of successes)

I'm not going to pretend that the whole world is a perfect land of equality, but just wanted to get you thinking in a way that makes it a little clearer what to do. If you had a bunch of concrete facts proving they are sexist pigs it would be a lot easier for you to recognize that these few people are just assholes and another company won't be like that. But if you just have a perception that the industry is sexist, the only option you will see is a total escape.