Player A has a Minsc & Boo, timeless hero’s and they have chosen to make a token and upticked to add +\+ on their first turn. The next turn played A moves to downtick Minsc and Boo, sacking the token to deal that much lethal damage. Am I able to respond to the loyalty ability being activated after the Loyalty counters are added by destroying the token with a card like Fatal push and stop the sacrifice from occurring?
You can cast, for example, Fatal Push in response to the "-2" loyalty ability, that is, after the ability is activated and before it resolves (C.R. 117.7).
But Fatal Push doesn't counter the ability itself, but note that the ability's controller must sacrifice a creature when it resolves if possible — it's not optional (see also Misdirection and compare Minsc & Boo with Grist, the Hunger Tide).