One could be exempted for religious reasons, which usually involved alternative service. Or exempted from serving in a combat arm. There was a case called United States v. Seeger in which Pete Seeger was the lead defendant, holding that exemptions were also available because of secular beliefs. A friend of mine was a co-defendant in that matter, an anarchist and pacifist named Forrest Britt Peter.

You could get deferred on the ground you were against war. You could not get deferred on the ground you were against the Vietnam War. A former friend of mine also managed to draw a 5-year sentence, of which he actually served two. As he described it the Judge, a liberal, came to his cell and begged him to accept alternative service or argue for deferment on the ground he was against all wars. He told the Judge that if he had any courage or principles, he would release him. That didn't work.