You made the right decision to take the project even though there are certain people who will make you uncomfortable. You can do the job professionally and according to your job description. If later he/she ends up leaving the project for one reason, that's something you can't control, so maybe that's for the best. I think we can't always get compatible coworkers, but don't focus on that, just do your job professionally. As you mentioned, we are mature enough to get involved in emotional things rather than realistic ones.
Break a leg!
Yeah we will never get the perfect team, so the best thing that we can do is make sure that we give it our best try to work with people we may have disagreements with. It helps is build and develop as people and professionals!