If your vehicles thermostat is stuck in the open position then it's okay to drive the vehicle when the thermostat is stuck open.
When you drive your vehicle with the thermostat stuck open your engine just doesn't build up enough heat inside the engine because coolant will flow faster through the engine so you heater may not work as well with a stuck thermostat that is stuck in the open position.
But if your vehicles thermostat is stuck closed then you should not drive the vehicle with the stuck closed thermostat because it will allow the engine to overheat.
If you have to drive the vehicle and the thermostat is stuck closed you can simply remove the stuck thermostat until you can get a new one and then replace it with a new thermostat.