So I wanted to run a stage RTA of a level that has a C5 entrance and a C6 entrance. The C6 entrance saves some time on a few stars, so is it allowed to go to C6 to enter the level from there or do I have to do the whole stage from C5?

Stage RTAs and singlestars can be started from any entrance, unlike savestateless completions. You can see that in Treasure World, where runners will start a Crumb Climb stage RTA from Wall Wall Mountain, or a Sky High Castle RTA from Autumn Memories.

Nice one! Thanks a lot Iwer!