I am probably the least qualified to opinionate on this one, (not a vet, or an American). But what the hell, what is the internet for?
Do I find it totally appropriate? Nope. But it is cute.
Do I have a problem with it? Nope. I see America. At least what a foreigners idea of what America is. The land of freedom, opportunity and expression. One of the few places on earth where one can not just hold, but publicly express, ideas and opinions that would be deemed illegal, as well as arrestable, in most of Europe. I don't know that man, or why he joined the military. Maybe he was burning with the love of his country, maybe he was underemployed and the military was the only job he could find. Who knows?
I see an American, demonstrating his rights. I see a father who loves his child. The people who don't like it? Are also demonstrating their right to protest, expressing their freedom of opinion.
It is cute though.