Look, what if everyone on Teh Dope had that attitude? We’d have “2,344 views, 2 replies” next to every thread title.
I say go for it. Fine with us if you look stupid.
Not quite. The Selective Service System still exists, and young men are still required to register with it.
It is possible to be exempted from military service for religious reasons, but it ain’t easy. You can’t just suddenly decide you’re a Quaker the minute you get your draft notice. You would have to prove membership or longstanding association with some religious body which prohibited all participation in war, and some kind of alternative service is often required. People have tried to get exemptions based solely on their personal philosophies or religious beliefs, with varying results.
Of course, you could always just tell 'em you’re gay. 
A guy I knew back in the 60s just swallowed a lot of aspirin and had some friends take him to an emergency room to document his “suicide attempt.” It seems to have worked.
I seem to recall a very longwinded song that ends with a man being told he isn’t moral enough for the army because he was ticketted for littering.
…And creating a nuisance.
There is the conscientious objector out that anyone can try. You don’t need to belong to a pacifist religion, but that would obviously help with your bona fides.