Wearing the uniform is not presently illegal, and should not be, depending on the context. Similar to “impersonating an officer” laws, there’s a line between dressing up as an officer or soldier for a Halloween or S&M party or something, and going out and stopping traffic. The first act should be protected under the right to free expression. The second, not so much, any more than one is free to shout “FIRE” in the proverbial crowded theater.
Claiming congressional honors as one’s own is presently illegal, and definitely should be. We’re not talking about showing your father’s or grandfather’s medals, even wearing them, if you say you’re wearing your father’s or grandfather’s medals; nor are we talking about wearing one of those knockoff Semper Fi rings you can get for under $10, or a T-shirt falsely proclaiming “I’M A VIETNAM VET 1967-1968”, which would be protected under free speech laws; but something more along the lines of claiming veteran status for treatment at a VA hospital.
Clearly there is honor and prestige uniquely accorded to those who have been given these distinctions, or this clown wouldn’t have tried to claim them.
In other words, fooling your classmates by playing dress-up is assholery. Stealing from Congress is illegal.
ETA: I voted “non-military background / definitely should be illegal”, because in case of ambiguity, I’d rather it be totally illegal to impersonate an officer or decorated veteran than to leave the door open for open season. To me the downside (complete disregard for the meaning of the uniform/medals because “anybody can wear that”) is far worse than the upside (“hey, I was just kidding, ya know, cut me some slack”).