These guys are Modern Orthodox baalei teshuva, of whom at least one regularly performs in non-Jewish venues (as well as Jewish), so they probably look at this in a very different way than the majority of the people commenting here. They dressed the way they did because they’re not trying to hide their identities- to them, there’s no contradiction. They’re coming from a completely different frame of reference.
Bear in mind also- while they’re already earning side money from this (Josh performs freelance with the Maccabeats, and Ilan is in the YU a cappella group the Y-Studs [don’t ask]), this is also a great way for both of them to get good publicity- which they’ve obviously already gotten in droves. Even if they’re eliminated in the next round, they’re set for life.
And, of course, I’m sure they’re having fun 🙂