Soulists do not believe in social contract theory. The social contract was invented by Enlightenment philosopher John Locke, the "father of liberalism". Locke was a capitalist. Soulists are anarchists. We don't like liberals.

I do have some philosophical disagreement there. I'm roughly an anarcho-syndicalist by ideology but don't believe in the plausibility of an anarchic society in my lifetime. Tools of the oppressors can still have value. Social contract, at least as nomenclature, is a very useful tool for describing and theorizing around social cohesion in a non-hierarchical society. In order for humans to coexist in a mutually beneficial manner, they need to agree on "constants" that can be deemed objective. Without this, there can be an "impedence mismatch", to draw an analogy from electronics, that can cause undue strife because of a lack of agreement on ethical basics. "Social Contract" can be a useful term/concept for describing this, even if not agreeing with the content of it proposed by liberals.

...While a social contract theorist would happily deal with a Nazi who was polite, well-mannered, and followed all the rules, a Soulist would not.

Here, I'd disagree with scoping. I think that you have put all who use Social Contract in the group of (neo)liberalism. I do not find this accurate. As I stated earlier, it is useful as a tool for describing basic ethical "constants" to enable social cohesion.

A Soulist would pull out the baseball bat and tell the Nazi to get the fuck out, no matter how well the Nazi follows the social contract.

Under an anarchic "Social Contract", that would be the correct action. Those wishing to enforce unjust social hierarchies, inflict suffering sadistically, and commit mass murder would be violating "Social Contract" (not just under most forms of anarchism).