I haven't experimented with Chess960, and I'm not actively writing chess engines right now.
But if I understand correctly, there isn't much difference between it and standard chess, just that the starting position and castling moves are different.

Perftree doesn't care about the specifics of how a move is performed, it doesn't do any position calculations itself. It just identifies a position by some starting FEN and a list of moves in UCI notation, and passes that information to the engines (your engine and Stockfish). Then the engines do all the position calculations.

So, if Stockfish can recognize the position as Chess960 and your perft script configures your engine for Chess960, then it should "just work". Or maybe Perftree just needs a small patch to configure Stockfish for Chess960 mode.

The problem is that Stockfish handles normal positions and Chess960 positions differently. You can see that with the following position: Qr1krb2/1bpp2pp/4q2n/pp2pp2/4PP2/2P3P1/PP1P3P/NRBKRB1N b Beb -
Without setting any options, Stockfish thinks the result of perft 1 is 43 but when sending setoption name UCI_Chess960 value true before setting the position, perft 1 is 42.
Fixing this shouldn't be hard and I might be able to make a PR soon.

I missed the answer, sorry for the late reply.

Exactly what @GreatGodOfFire said. The main issue I think are the castling rules in Chess960. In the end I made it work by patching it locally and sending the setoption command. Thanks for the help!