Um... Ghost Rider appeared to be trying to kill the rest of the party, to the players as well even if not all the characters thought so.

The issue here is that he's bragging about killing people, and not like he fights them or something and they're his enemies. He's not just saying "kills and feeds on his enemies" or something. That'd be fine, if kind of uncomfortable especially given the other stuff he does but it's not like Saber wasn't already uncomfortable with him. He's openly saying he kills anyone. As far as Saber knows, a vampire doesn't actually have to kill in order to feed, as well.

At the very least they're going to want to subdue him if nothing else.

But I [i]don't[/i] want to just start a fight right now. I don't want to get into trying to kill a player character.

The mildest reaction I can think of is trying to be as slow about it as possible and having Saber verbally confront him about it before attacking since that at least gives a chance for... something to happen before there's an actual fight, though I don't know what.