They're the personal ones. People who don't believe gays should be allowed to be married by the state. People who don't believe women or minorities should be allowed to vote. People who believe all immigrants come here to kill/steal/crime whatever.
The difference is when it's an institution (private versus public schools for example), that's pretty easy to disagree over. One side does not believe the other is inherently evil and a 'lesser' person. When it's about individual rights, and an attack on you as a person, and your inherent rights as an individual, that is almost impossible to overcome.