If an in-the-closet "gay" Republican gets the nomination, we can be sure the Left will try to make a big issue of it, probably by spreading rumors of GOP discontent (thereby simultaneously knocking off the Republican candidate while making Republicans look "intolerant").
When was the last time you heard Dems say anything about sexual orientation of a candidate post primary? You don't, even in conservative states. They are capable of a lot of crappy things, but that hasn't historically been one of them.
These things usually occur in a whisper campaign, prior to the primary, benefitting a candidate without much appeal - sometimes originating from the Dem committees which want to manipulate the GOP electorate toward a particular candidate who they perceive as weak.