That's not true, I'm afraid. Anti-war vets have a tendency to stand out because they are anti-war and because they make for the most effective and threatening anti-war activists (threatening to the status quo, that is). People like Smedley Butler and Scott Camil come to mind.
But let's not fool ourselves... they do not represent the majority of vets. I grew up in a place where war vets were a dime a dozen, and if any of them were anti-war they sure as hell never talked or acted like it.