Yes, a real band. They were really popular among the indie-folk-pop set around the turn of the last century. The bit on parks and rec was just a way to establish April’s character as ‘too cool for all you bitches’.
Pretty good stuff if garage studio music is your jam, but if you haven’t heard them yet, they may sound derivative because they did influence a lot of later stuff in that genre.
That would be a Radical Faerie.
Seriously check them out. It’s a cool and really influential group of pioneering gay dudes, gaying it up on the farm.
They have sort of died out as a group, but one can hold a pitchfork in a homosexual manner whenever you choose. That’s not illegal yet.
Radical Faeries