Ok, getting rid of the cultists is deceivingly easy. I just needed to talk to them outside the inn, Wuld away from them and enter the inn to avoid getting killed.
Oh, I couldn't help to notice that LiveSplit doesn't quite work with SSE. The auto-pause doesn't work and the RAM watch is always empty. I suppose they're not compatible and that's just something that I have to live with. D'oh well...
I could try to run very far and wait for something like 3 hours and then just fast travel back to Riverwood. That would add something like 3 minutes to the run, but since I'm not trying for a world record it should work just fine. I'm following knifechamber's video and I'm going glitchless because I'm assuming it takes less training overall, since glitches look very hard to get right. At the moment I'm still struggling with the very first jump over Alduin's wing on Helgen, so a whole run of that would just wear me out. Either way, thanks for the help, I really appreciate it.
By the way, thanks in advance to anyone who took the time to read this :D
So I'm running SSE Glitchless Legendary and I've stumbled upon something I didn't expect for the run: The cultists go after you in Riverwood and go as far as inside the Sleeping Giant Inn to murder you, and since I'm basically following an youtube video (that didn't seem to stumble upon any cultists) I'm kind of stuck. I've seen other posts saying that it is a bad idea to run SSE, but that's what I got and I don't intend to purchase the original just to run; I bought SSE before I got into speedrunning.