I think if you asked my students to name one single value that I hold, passionately, they would say: "She HATES lazy relativism." I deliver my diatribe against lazy relativism in every class-- usually multiple times-- to the point where I actually feel sorry for students who have taken my classes more than once and can practically recite the speech themselves. "Lazy relativism" is the kind of thinking that never bothers to account for itself, that can't formulate its own principles, that won't try to settle disagreements, barely even engages in disagreements, and which runs and hides behind completely lame acquiescences like "well, what's true for you is true for you, and what's true for me is true for me... so, like, whatever, dude."
The thing that bothers me the most about this kind of attitude is that, more often than not, the people who adopt it aren't actually relativists! That is to say, most people who resort to lazy relativism actually DO believe that their beliefs are true (even "True"), and that people who disagree with them are wrong, but they haven't thought through the justifications for their particular positions or values in advance and can't seem to be bothered to do it on the spot. Conveniently for them, we also live in a culture in which bad faith tolerance-for-others is ubiquitous and rewarded, while productive intellectual sparring is shunned, and they regularly confuse "defending one's position" with "imposing one's position." They don't want you to impose your silly falsehoods on them, and so they will ever-so-condescendingly refrain from imposing their Truth on you. Noblesse oblige, I guess. As anyone who watches television knows, political discourse these days only models this ridiculousness. Talking head on one side, talking head on the other, each spouting pre-fab position statements. Nobody talking to one another.
In my more patient moments, I try to get students to see the fundamental contradiction at the heart of lazy relativism. If I think that torture is morally impermissable and you think it's not, neither of us can also believe that we're both right. If I say something like, "well, I think it's wrong, that's the value that I hold, but you can believe the exact opposite and that's fine with me, too"... well then, frankly, I DON'T actually hold the value that I am claiming to hold. Of course, I can operate with a more robust relativist sensibility, in which I am willing to grant that I don't have any special access to Absolute Truths (or that there are no such things), but if I really believe that, then that only increases my burden of responsibility for giving some account of my claims. Or it requires me to stop using the language of values and judgments alltogether.
Values shouldn't be easy things to hold, and if we can't hold onto ours when they come into conflict with others, then we ought to let them go. But we can't maintain any meaningful sense in the phrase "I believe x to be true" if we also allow not-x to be equally true. Not to get all law-of-noncontradiction on you or anything, but rules are rules. I prefer interlocutors with whom I totally and completely disagree, but who will own the passion of their convictions and translate those into discourse and action, over interlocutors who don't want to disturb the peace of parlor conversation. And I am, for the record, a relativist.