I would classify myself and most of the people in my social circle as pretty darn liberal. I don't know of anyone who has actually refused to talk to someone or cut a family member out of their lives based on their political affiliations or beliefs. That's both impractical and immature. And those people who wouldn't give their neighbor a ride home in the rain? That's awful. Do better.
But, I will say that I do have a harder time relating to the people in my life who support Trump. Not so much because they support Trump per se, but because of the beliefs and values that lead them to support Trump.
For example, my in-laws are big Trump supporters and, for the most part, we just don't talk about politics anymore. But that doesn't erase all the differences in values and worldview that lead us to our political beliefs. For my husband's and my part, we're atheist/agnostic, concerned about environmental issues, are skeptical about corporate power, and like that we live in a place with lots of immigrants and people of different cultures. My in-laws are deeply religious, concerned about government overreach, and think that immigrants should assimilate to their view of traditional American values and the country would be better of with fewer immigrants in general. These are extremely different value systems and lead to different lifestyle choices on everything -- how to spend a vacation, what to eat for dinner, what kind of schools are best, how to celebrate holidays.
I don't think they're bad people, although since Trump came onto the political scene in 2015, they have said some things about immigrants and people of other races that were alarmingly cruel. They have mostly been kind to my husband and me and they love our children. That's really the only common ground. We stay in each others' lives because of our children.
When they are at our house, I make an effort to do the things that make them comfortable because they are guests and that's how I was raised to treat a guest. We raise the thermostat, go to church, eat more meat, let the kids watch more TV, drive when we would usually walk. When we're at their house, we do basically the same stuff, but I have noticed small accommodations they have made for us--like having fresh vegetables in the fridge. They do actively thumb their noses at our values on some issues, such as by ignoring our request for fewer gifts and proselytizing to our kids, which I don't appreciate. My husband and I try to stay positive about it to allow the kids to have their own relationship with their grandparents, but it is hard.
So, no -- I wouldn't cut someone, particularly a family member, out of my life because they supported Trump. But I do think political beliefs are a reflection of someone's values. And someone who supports Trump probably has very different values than I do. And, naturally, that makes it harder to have a close relationship.