It's an interesting idea. I can certainly agree with Charlatan on being able to quickly discern someone whom I won't get along with at all, and I've also been in situations where I've met people I could almost immediately tell I'd get along with, but I really don't know that it runs to the extremity of Soulmates.
But maybe. If I believed in soulmates, I guess it could almost logically follow that I'd have an anti-soulmate. But the spectrum of people in the world is so wide, I don't see it needing to be anything so minute, as being "one person." Nor do I see a need to spread any kind of discord by saying, in effect, "this person is my enemy."
Especially when I can just as easily spread nasty gossip about them with a shit-eating grin on my face.
