Whether I will associate with someone with profound differences in beliefs depends on what those beliefs are and how open they are to changing them. For example:
I don't mind associating with Christians in general. I do mind associating with the narrow-minded, intolerant, homophobic ones.
I don't mind associating with conservatives in general. I do mind associating with the obnoxious, hateful, not-all-lives-matter ones.
I don't mind associating with progressives in general. I do mind associating with the "establishment is bad," Bernie-is-our-only-hope, "**** SJWs," omnivores suck, etc. ones.
In general, I don't mind disagreements in beliefs. But I have two rules:
1. Your beliefs MUST not dehumanize any groups of people in the slightest. If your beliefs do that and it is pointed out to you, you MUST react nondefensively and in a manner that shows you are going to immediately fix this blind spot of yours, regardless of how uncomfortable that is to you.
2. You will not be all-give-and-no-take. If you wanna dish it out on me and try to criticize what I believe in, so be it, but don't you dare get upset when I return the favor.
I've cut some people out of my life that failed these simple rules. When I look back, the only regret I have about that is not doing it sooner. Toxic people are not needed in your life.