There’s a difference between claiming to have served in the military and claiming to be a favored minority: one is the dishonest claim to an accomplishment, and one is not. However, even in the veterans’ case, eventually the point has been made, and further marches or caravans or whatever are unproductive.
One of the problems with our society is that people have been taught to be “proud” of non-accomplishments, so that we now have whole industries devoted to creating a sense of entitlement based on breathing, rather than respect that is earned through good character and achievement.
Like being American for instance.