I am taking the switch for the garbage disposal off of an outlet, to make the outlet always hot. The wiring has a red, black, white and ground. Do I wire nut the black and red (hot) wires together then pigtail it into the new outlet?
Probably the red wire is switched hot and the black wire is always hot. You should not use both, just select one, probably the black. Assuming you're using a new outlet without the tab broken, just connect the black, white and ground; cap off the red wire with a wirenut (add electrical tape if desired). If the result is that both receptacles are switched, use the red wire instead and cap the black instead.
You don't want to connect both the red and black since if they don't originate with the same breaker, you have a Multi-Wire Branch Circuit (MWBC) where the red and black are actually opposite legs for your 240V house feed. In this case, connecting them together will trip your breakers (best case) or cause a fire (worst case).
Are you actually removing the switch (putting on a blank plate)? In this case, instead of changing out the outlet, you could simply remove the switch and connect together the wires that went to the switch (not the ground wire).