What needs to happen here is pressing the button needs to immediately register the press elsewhere in the code. The UI animations and the button tap should be decoupled entirely.
Then the user can tap away as fast as their heart desires and only the animations are going to continue on. That’s an easy problem to solve... by doing as you say and aborting them or shortening them.
But you should NEVER have UI animations and effects block your logic path. They should be parallel operations not serial.