Why do many interviewers talk about "respect" when my military service is brought up during an interview?

A lot of what we were trained to do in the Army out of necessity doesn't translate over to the civilian world that well. As an example, being brutally honest to your superior in the Army, as long as it's presented within protocol, is acceptable and even encouraged. in the civilian sector, however, brutal honesty can come across as being over critical. It could be something along those lines.

I also noticed, at my own workplace, that many vets will start bsing with each-other on the job (things fellow vets wouldn't think much of but others within earshot could see as HR worthy) This might also be a factor in what they are referring to.

There's also a fair amount of vets who have a short fuse (I'm one of them at times) which can be a major no-go for social interactions period let alone in the workplace.

Maybe they are hoping that your level of respect will bleed onto those at the job that show little (if any) respect?

In my opinion, that translates to "..at this company, we do things differently. Are you willing to adjust your style to fit our "culture"?"
The next time you're asked that question, ask the interviewer politely to clarify the question/statement to ensure you respond appropriately.