Can I use compression connections on rigid "L" copper?
Compression style stops work the same on Type M and Type L, they both have the same outside diameter (O.D., 5/8").

Type M is thinner walled and (IMO) substandard. It is cheaper for a reason, you should use Type L.

As a sidebar: it seems you are familiar with soldering since you are plumbing the bathroom yourself, so why would you use compression (or "Sharkbite") connectors? It will just set you up for difficulty when (not if) the stops start to leak-by later on and you have to replace them. Solder male adapters to your stub-outs and use thread-on stop valves.