I'm sure some kids from the IU ticket office are into stuff that would make you cringe.
I bet you're into some stuff that would make other people cringe.
Why wouldn't you let a drag queen or otherwise trans person watch your kids? Because they make you uncomfortable or because you're afraid your kid will be abused? If the latter, why do you think they're more likely to abuse your kid than say a church leader, scout leader, or sports coach?
I 100% get that cross-dressing makes people uncomfortable. I have that initial reaction too. But then I have to challenge myself as to why and it's honestly just because it's unfamiliar to me. Just like it was the first time I met an out gay person. Now some of my best friend's are gay. NOT being weirded out by something and judging a book by its cover, so to speak, takes challenging your comfort zone and realizing that someone being different and weird based on your experience doesn't make them a bad or dangerous person.