Here’s my take on that, and this is just my opinion that I formed around the time that all this happened and maintained up until I ended up in the same situation. I make no certifications about absolute correctness of timeline and events - this is just my recollection and impression.
There is Cassius Clay, and there is Elvis Presley. Both Elvis and Cassius were of that certain age during a time of drafts, military service requirements for able-bodied young men, and they were relatively qualified to do that service.
One man, Elvis, suspended a rocketing career and did his time in the Army; he exited the Army and picked up his career and propered. The other man, Cassius, became a Muslim and changed his name to Mohammed Ali and joined the world of peaceful Islam were he became a conscientious objector refusing induction and actually got nailed and convicted for draft evasion (later overturned by USSC).
Released from that conviction, Mohammed Ali was free to continue the peace of Islam by climbing into the ring and continually slugging it out for mega dollars.
As for myself, I served during Vietnam, not in Vietnam though, in the Navy. I told my sons that if things had been different and I had been drafted, I would have picked up my rifle and gone to war.
As for Ali, I will sympathize with someone who is truly a conscientious objector. But Ali evaded military service, ostensibly as a C/O, and then made a living, engaging in violence, beating the crap out of people. What a phony.