The few times I've ever cut someone off, it was because they disrespected me. I don't ask for agreement, just respect, and that's what I am willing to offer. If I cannot respect someone, then it's an issue of integrity for me to be friends with them; it's not sincere.
I'm more tolerant than most people, and that's saying a lot, as I have high standards and am serious about keeping integrity. So most people will decide I am too different from their preferences long before I would ever decide that. I'm really comfortable with not agreeing, and I rather enjoy exploring different perspectives. I like intellectual debate and am not weirded out easily. Of course, respect is still in order.
I rarely make this decision consciously. I tend to respond to things as they arise.
If someone makes effort with me, then I respond to it or I ignore it. I don't experience it as making a decision, so it's hard for me to say I'd ever think in the way you're describing it.
I will say that I don't feel compelled to invest a lot of emotional energy into most people, and so I may seem to hold them at arm's length, and I guess I am making some judgment that they don't have any potential to mean a lot to me. Some of this may be a matter of values, lifestyles, interests, etc.