The Greatest (your e-mail)From Jason, and this is quite informative:
While I'm sure you'll get plenty of mail about him, I figured I'd throw in my two cents worth of knowledge as well.
Probably the first important thing to note about Ali and the draft is that in 1964, he was disqualified entirely from military service. The reason behind this was failure to meet academic qualifications. As Vietnam dragged on, standards were lowered to meet troop requirements, and in 1966, he was flagged as eligible, classified 1-A. Here's a pair of news articles about it from back then:
The other thing to note is that he never refused to report. He did in fact report, and claimed the status of being a conscientious objector. Ordinarily, anyone making that claim is barred from service entirely, and such was the recommendation of the local draft officer. However, that claim was overturned by the DOJ, and as near as I can tell, the reasoning was never revealed. He did ultimately report in 1967 following a rejection by the draft board to grant him ministration status(which was granted to Mitt Romney in order for him to serve as a missionary in France, so there's definitely precedent). However, when he reported, he refused to step forward, and was subsequently indicted and convicted.
From there, we go to the SCOTUS decision in 1971, where the lower courts decisions were overturned due to the fact that the draft board failed to state the grounds on which Ali's status as a conscientious objector, as well as a minister were deemed inapplicable, and they ultimately issued a unanimous decision from 8 judges, as Justice Marshall recused himself due to his previous status as Solicitor General.