I don't know. Maybe I'm just mincing words, but it does seem like if you disagree with someone's belief, you are (at least implicitly) criticizing the validity of that belief. If you disagree with someone's behavior, you are (at least implicitly) challenging the appropriateness of that behavior. So I'm not sure I agree that disagreement and criticism are entirely distinct, or that they are different than judgement. Of course disagreeing with/criticizing/judging someone's ideas or behavior is different than devaluing or condemning the person, themselves, which may be what you meant by personal judgement.
If someone you spend time with does something to annoy you, do you never tell them so? What if, in your opinion, they're doing harm to themselves? Do you still let them be themselves, to their own detriment? What happens when you feel so strongly about it that it begins to jeopardize the relationship? What happens when a problem comes up that's so big that it's impossible to ignore and you're forced to make a choice to either voice your criticism or abandon the relationship? (I'm not necessarily talking about giving someone an ultimatum but, rather, telling them how you feel? Talking about your differences and coming to some kind of understanding rather than leaving things unsaid?) Do you really never compromise or criticize, or at least never until the relationship has absolutely ended?
I have no idea what you expect of me other than to repeat what I already posted, because that's exactly what I meant to say and exactly how it is - or at least my perception of how it is - and the way my admittedly few friendships and my relationships with people work.
You also inserted 'beliefs' into your argument which was not what you had originally specified, but I can say that if, for example, I have a friend who is a fervent believer in a god of his choosing, when I am not, or who is a Republican, when I am not, I respect their viewpoint, and listen to their reasons, but have no desire to try and argue them around to my view instead. However interested I am in their viewpoints, arguments or beliefs, and however much I might indicate where mine differ, there is no criticism, implied or stated, nor judgement. It is a purely intellectual engagement of ideas as far as I can tell. There is plenty of talk of 'differences', in the sense you seem to mean of differences of opinion, but the understanding we look for isn't in moving one another to a single viewpoint, it's in understanding the difference itself.
As for 'what happens if....', I think perhaps you misunderstand the nature of my friendships. It is possible for someone to annoy me I suppose, but my friends don't. I think that's not because they specifically try not to, but because my friends are people who are as respectful of me as I am of them. Hence were something to happen which might cause a problem, I would likely presume it unintentional (in regard to me, and/or the friendship) and leave it unremarked because it is not remarkable, or at most, simply state what the issue was, and leave it at that.
I have certainly never had reason to criticise a friend, and that seems such a strange notion to me that I find it hard to imagine a reason why I would.