I went through the same exact thing with my parents. They okayed a therapist, but said the same thing, they didn't want him to be "biased". I also didn't have a car or a job. They did let me pick the therapist, but they wanted me to stop seeing him after the first session b/c he was polite enough to ask me how I would like to be addressed pronoun-wise.. I had to literally beg to go back each week. But they eventually got over it.
Be careful with who they pick though. If their idea of an unbiased therapist is just a regular one who doesn't specialize in gender you'll probably be fine. Most are understanding. But if their idea of an unbiased therapist is the same as my parents' was (like somebody from NARTH) then you may be better off waiting until you can see who you need to see. Somebody telling you that you are sick or wrong, or mentally disordered during every session, and telling your parents that you are at this stage of the game would do waaaaaaaay more harm than good.
