What are the stigmas attached to veterans seeking mental health counseling?

Personally my advice is that if you need help, that you should go out and find a shrinker and pay out of pocket for it. If you are a federal employee it will flag you if your bluecross is getting charged by a shrink ( I got a real fun story on that one, it starts with seeing a shrink to get some drama sorted and ends with a 5 year blackball by my command)
If you are enlisted...I've heard stories on more than one occasion about on base and well meaning shrinks having a conflict of interest between their patient and the command, so if you are enlisted I would suggest paying out of pocket as well and finding a shrink who has no such conflict of interest.

I'm going to say that 60% of the people out there don't care if you are seeing a shrink, but when mass shootings happen well...it raises anxieties and people do funny things when anxieties are raised. People will start talking, people will start to read things into even the slightest of outbursts, and from there it is a matter of the rumor mill, because unfortunately people also like to talk and the more sensational the story the better.

As for active duty, there shouldn't be, however there are circumstances that might make someone hesitant to do so. First is divorce proceedings. If you're going through a bitter divorce, it might be used as ammunition against you, particularly if children are involved. Another is for potential civilian employment in public trust positions. Any perceived mental instability might preclude you from a career in law enforcement. Lastly security clearances are fickle. Psychological difficulties might stop you from receiving a clearance.

I see those that seek mental health treatment in any form as responsible service members. if you recognize your mental state may have a negative effect on your team and you seek counsel, i applaud you. this is how we stay sharp when need be.