Principal Hawkins made up the story about how he had no luck on dating apps as a school principal who likes Broadway.
He's good-looking enough that woman wouldn't read his profile and those are generally considered attractive qualities in a man anyway. He probably just has been too timid to put himself out there. Trent's sexuality may never be stated in the show, but he might be trans.
Is this solely based off of the line, "I accept that I was born a handsome man," from the Acceptance Song? Yes. While this could just be him bragging about his appearance, considering that this is a song about acceptance, this troper likes to think that Trent had to come to terms with his gender identity and is all the happier for it.