> I was interested in jobs that would likely require government security clearances, and (I don't know how true this is) I had heard from multiple sources that a history of seeking help for mental health issues may disqualify you

FWIW, you heard correct. This is true. (I don’t have any clearances myself, but I did work for a major defense contractor in the past, and a family member has some sort of above-top-secret clearance for his work.)