Most libertarians go apesh!t at the thought of a draft.
Personally, I don't have too big a problem with it in times of necessity such as the Civil War, WWI&II, etc. Such drafts would be for the duration of the necessity.
I also am not too incensed over low-scale drafts for countries that need a large proportion of their population trained & organized in the military to survive any serious conflict.
I might even be persuaded to support a draft in the 'States, given the right restraints/conditions.
Where I do not support it is something like the old czarist 25 year service draft, which was a functional death sentence or the press-gang type drafting.
Given all the above, I would reserve to the military the right to refuse any draftee or volunteer as unsuitable. The purpose of a draft is to provide manpower to protect the existence of the country, not provide make-work or provide unsuitable folks with a self-esteem boost by allowing them to contribute.
The dude pounding on the army keyboard & lifting paperwork has been, in extreme circumstances, the same guy who was rounded up & rallied to pull chestnuts outta the fire. So, yes, even army paperpushers need to meet a certain physical standard.