Do you think putting military experience on a job interview makes employer skeptical about you possibly having issues and not hiring you?

I once had an interview. The first words out of the facility managers mouth was "You seem a bit overqualified for this position." To put some background, it was for a phlebotomy position and I had served 8 yrs as an Army Medic. But at the end of the interview, I was then asked "Give me a reason why I should hire you over the next person." My answer was that my experience speaks for itself and less training will have be to performed with me.

I think it might depend on the type of job and the employer.

I'm going through this exact samething. The best answer I have found is that it's a business, they make money, and they will hire the person they believe will be an asset to their company to improve business. Do the best you can to make them see you as the best assets. That being said, it tells you they're all about professionalism. Though that always isn't the case, as in the military, there are some who bring their personal feelings to the table. They might pass over your application. Best advice is to civilianize your military experience and what you bring to the table as much as possible. Be relatable and write your resume to fit the job you're applying for.