Think it's fair enough to refuse to go and state why.He was fined 10000 and banned from boxing for 3 years.
Also he had been deemed unfit to serve in the army under the original draft terms.
His IQ was in the bottom 10 percentile or something. We think of Ali as this fast talking quick witted motor mouth but he likely enough had significant learning difficulties and the public schools in Kentucky in the 50s probably weren't the best.
His prospects if he did go were that he would have gone though basic training and then done a load of exhibition boxing matches to entertain the troops and done some recruitment promotion work. A bit like Elvis.This was all spelled out to him at the time. Chances of him seeing fighting were about zero.
He applied for conscientious objector status on the basis of his religion but that was rejected, so it is perhaps technically true to say he dodged the draft I wouldn't consider that he did.
In the circumstances he took the much more difficult, costly and I would argue, courageous route.
Incidemtly the famous line "No Vietcong ever called me N.." was said out of frustration as he was doorstepped by a bunch of journos when he was Tired and pissed off after weeks of public speculation..You can take it that it was his honest response
I should also say his religion is problematic enough. A weird branch of Islam mixed with scientology. they preached racial segregation and believed in Alien overloads colonising the earth to benefit the "black" race. I don't know if they have many adherents any more
The Thomas Houser Ali book is well worth reading on this stuff.