Nope not normal it means either your shift linkage bushings are worn or you have a worn engine mount as suggested. Try ‘rocking’ the car forward and back while it’s in gear and the engine is off as you watch the engine and it’s mounts, once you get it moving you’ll be able to see the engine move, if you see excessive movement check the mounts for cracks or damage. Obviously leave the parking brake off.
If the mounts are OK then check the shift rod going into the transmission just above the exhaust, move it around with your hand, there should be NO play in those bushings if you find any replace the rod. Unfortunately this means dropping the exhaust and the heat shield but it should clear the problem up.