No, of COURSE requiring a photo ID to vote would not be unconstitutional. But if it is, so also it is for buying or selling guns, including Class III items.
I was wondering if you knew where voting issues might be found in the Constitution.
If the feds were to get involved in this, then the Constitution would need to expressly support federal activities along these lines.
Otherwise, if this were just a state issue, then the Constitution would have to expressly prohibit this kind of state activity. If not, states should be able pass voter ID if that's what the people of the state choose.