Humanize them: We are all individuals with our own hopes and dreams. No one can completely walk in your shoes. Recognize that other people may have different motivations driving their opinions, a different hierarchy of issues. If all else fails, see the hurt inner child they may have inside.
Find something in common: Find something, anything, that you can talk about if you need to be around this person. Even supervillains might have a cute puppy at home.
Agree to disagree: Definitely stand up for your beliefs, but don’t go into a discussion thinking you can change someone’s mind. Half the time, we aren’t even listening to what the other side is saying. We listen enough to formulate our counterpoint and that’s it. If it’s a person that you want/need to keep in your life, maybe a change of subject can help.
Fill yourself with love and peace: Be so full of grace that nothing can impenetrate you. Meditate. Pray. Listen to music. Get out in nature.