A lot of other things can make you unelectable too...like...

A not-so-pretty face. A vague resemblance to Herman Munster. Bad hair. A poor figure. A high voice. Not belonging to one of the two major political parties. Being female. Being non-white. Being a Jew. Being a Muslim. Being perceived as an "intellectual" rather than one of the common people!

All those, in the past, have made people unelectable as President of the United States.

Being Catholic used to also be a no-no till John Kennedy managed to overcome it.