No, being gay isn't but LGBT organizations and the Pride Parade definitely is. If you don't want to call it an ideological movement you cannot deny it is sectarian. It does go a little past equal rights I'm afraid. I use to watch the festivities from the street corner or my living room window when I lived on Halsted -- the main drag of Chicago's Pride Parade. It is always a heady mix of pomp and politics, and of course partying. There are delightful moments and disgusting ones, it is quite the sight if you've never actually been to one in a major metropolis.
Personally, I don't think either should necessarily be prevented. The military is our military, right? It isn't some foreign, separate organization that's removed from the people, right? (at least in theory) There are gays, church-goers, atheists, et al who comprise our military right? We're all citizens, right? Non participation is just as much a symbol of opposition as participation is considered a symbol of support. Our military is here for all of us and as such should support all of us.
The only problem I would have with it is picking and choosing. Since it is our military all have to be allowed, you can't deny all because this is a symbol than that the military and by extension the government is separate from the people who they're here to protect and represent.
