Are runs with Slippi considered mods if the only difference is it is on Slippi and you can use c stick. I assume yes. However, I would like to state it could be a really good way to let new players get into the Speedrunning community for this game. It would be standard also.

UCF is banned so no but I wish that we could do a c stick mod

Slippi is not allowed as the rules states you must use Dolphin 5.0 and no other emulators.

Also, if you want to use UCF, C-Stick and other mods, then go to the Category Extension leaderboards here: https://www.speedrun.com/ssbm_ce