It depends. As long as they're not one of those insane, PETA worshiping, human despising, "everyone must be vegetarian," "all animals must be free or dead" vegetarians then most likely not. It's an issue of core beliefs. I don't think I could completely love someone who had THAT much of a grievance with what I do, or people like me do. And vice versa: I don't think they could love me if I believed that part of who they are is that crazy.
I'm not saying people can't love each other and have vastly different opinions. Who knows, despite all this, my soul mate might just be one of the church of PETA. But I do believe there is a point where core beliefs become a large distraction in a relationship. If they can't stand to see me eat a turkey and ham sandwich, as I do at least once a week, and they aren't willing to give a bit then that's too bad. And I'm certainly not going to stop doing what I like just to compensate for them. Relationships are about compromise, not compensation.