Let's put the shoe on the other foot--if a Democrat who didn't have a four-year degree was running for the Presidential nomination, I'd have serious misgivings about casting my vote for them.
I have a master's degree. Considering that universities have been generous in awarding four-year degrees for several decades now, I expect my President to have obtained at least the same educational level as the Front Office Manager at the Candlewood Suites a few miles from my office.
But, I guess asking the person in charge of hitting the Doomsday Button to have a four-year degree in communications or whatever bullsh!t degree most athletes get is "elitist."
The fact that it takes very little effort to get a "bullsh!t degree in communications" kind of proves the point that there's no need to consider a college degree as a prerequisite.
The academic rigor for someone seeking the Presidency should be higher than said degree.
If someone who is running for President does not have a diploma beyond the one they received from high school because they either can't, or won't, finish their degree, they have not earned my vote.
People seeking far less prestigious positions are required to have obtained a four-year degree. I fail to see how demanding the same of our President is elitist.