Not necessarily,Jack. While I usually shoot my 870s RH, I can operate them very well from the port side.
I've big hands. A slight twist of the wrist means I can take the safety off with my thumb. I can reach the slide release with my trigger finger without breaking my grip. Can't do that RH.
Less endowed shotgunners may have probs, but I don't and I'm sure many others are the same way.