Would anyone care today? I'm about as right-wing as they come and I consider it comprehensively irrelevant. Certainly very darn few of his present supporters would abandon him because of illegitimacy.
Perhaps some of his present opponents would care, but nobody else.
It’s been a frequent topic in our house, with one party agreeing with you, and me believing that there are in fact people who would care. Certainly not his diehard supporters, but on the fence types who would not like the idea of a man who was an illegitimate child as president.
Probably affected by voter age.