Actually.... I think some in the public might have an issue with it. Heck, I know some in uniform who have an issue with it. I went to the wedding of a Navy lieutenant (USNR). He was upgraded to first class. And wouldn't you know, some active duty members weren't exactly impressed that a reservist was upgraded (it was assumed he was in uniform... but I don't really know).
I think the only time I flew in uniform was as a cadet, and that was generally on Southwest Airlines (where we're ALL first class!). It was much easier to ditch the shirt-stays and fly in civies (which also allowed me to relax... although in Baltimore I recently saw a very sloppy recent USNA grad sprawled out in uniform in the nice comfy chairs, fast asleep.... now THAT screemed professionalism).
Whether we like it or not, the military and its members are judged. If they're in uniform, it's already a free flight, but it's safe to say that there are probably individuals (maybe someone flying on their furlough day) that don't appreciate hearing about the federal government's spending issues while also watching someone fly first class (it's also safe to assume they don't immediately assume someone was given an upgrade.)
This is what goes with defending the public's trust. You get a free flight, but that means you don't also get a free flight in a super fun first class, or a reservation at the huge honeymoon suite!