I've actually felt a benefit from being male. In the healthcare system, female patients are sometimes viewed and dismissed as if they're just being dramatic. In all my time engaged in treatment programs, I've never once been made to feel this way. There have been occasions where I felt I wasn't being taken seriously enough, but I've never felt stigmatized by any healthcare worker I've ever encountered.
Of course, I also don't look like I "have it together." For anybody who lays their eyes on me, it's going to be apparent to them that I've got some kind of issues going on. I'm also more feminine than I am masculine, both in appearance and in mannerisms.
All along, I've figured that if I was female, there's no way I'd have gotten the same quality treatment as I have as a male.
I'd imagine if a traditionally all-masculine man went into a doctor's office and complained of anxiety or depression or whatever else, then that man would be vulnerable to being stigmatized with a "get over it" reaction as well. But I wouldn't personally know this.