Honestly, in my entire career, I have never encountered that. I started my career at the big show when civilian pilots were still a relative novelty (within the last 10-15 at that point), and I'd fly with two other guys (3 man airplane) where if they were milbros, they'd launch off on who knew who in what squadron, and I was essentially ignored unless they needed the temperature adjusted. Which was perfectly fine.
BUT I wouldn't just chalk it to to being a milbro. I encountered the exact same scenario on other aircraft when the Captain was a "local" and so was the lead FA. It was all about where you went to high school, what neighborhood you grew up in, and what sports team your kid played on, etc. But unlike the mil guys, who could care less about you, the local people were sometimes genuinely angry that you commuted, which I found bizarre because the local area was famously inhospitable to folks from out of state.