It has nothing to do with who is more or less deserving of support. That is an inference you are drawing on your own, not one that his fairly implied by the article.
It has to do with providing clarity as to what his position actually is. He is not against the use of those pronouns, but rather against government compulsion to do so. Whether a particular reader believes one or the other is the stance more worthy of defense really doesn't enter into it. They just don't want to misrepresent his position, so they add the "note". Else, someone is going to refer to him misleadingly as the guy who refuses to use those pronouns.
Else, someone is going to refer to him misleadingly as the guy who refuses to use those pronouns.
So he needs to add the note to guard against the possibility of someone else making a wrong “inference” ... “on their own”?
And just why is it even important to worry that someone might wrongly infer that?
Hence my inference.