I work for General Dynamics – Information Systems (GD), we are the primary contracting company for the Defense Intelligence Agency (DIA); both GD & DIA enforces a non-discrimination/harassment policies. Now working in the Intelligence community does require a security clearance, well working in almost any government capacity requires a security clearance & that means divulging all personal information (that does not include sexual or gender identity) but you must be hired by a company first and they don't dig that deep into your background.
Now, I had an interview once with a company that was the prime with NSA (National Security Agency), they have the same non-discrimination/harassment policies as GD & DIA but in the interview I informed the HR interviewer that I was TG (now the resume that provided to them during the application process had a female name) & the interviewer informed me of their discrimination policies & that the fact that I was TG would not play in the hiring of anyone, this was a phone interview. I didn't get the position, now it could be that there were more qualified applicants but I don't know. Plus I already had a position with GD I just wanted to see how other companies reacted to TG people & I guess I see. But if you have already transitioned and your name has been change legally then I don't see the problem, I know folks that have transitioned and has changed companies & have went to work as a Government Employee with no problems at all. So it may just be the company in which you apply to. My advice would be just don't give up.