Waiting for move animations to finish before you can interact isn't fun

[1j01]

You can technically cancel by undoing and redoing (ctrl+z, ctrl+shift+z) but that doesn't feel nice either and it's not particularly "discoverable" — it's a hack.
You should be able to select pieces, and probably even queue up moves, while it's animating. Need to consider selecting pieces that are currently under attack, and other board state consistency.