There's a difference between being mean directly to someone, and being indirectly mean (where you know it'll get back to them), and being mean *about* them, but somewhere you don't think it will get back. The first is honest, if mean. I find the second pretty despicable and I try not to do it. (I would say that I don't do it, and I don't recall doing this any time in the recent past, but I may well have. And if I have, my best friend is authorized to kick my ass about it. He keeps me honest.) The third ... gets me in trouble more often than I would like, and I would do well to remember that public is in fact public.
If you're in a feud with someone you personally dislike, especially if the feeling is mutual, knock yourself out. Be as mean as you want. It's not up to me to attempt to dictate what you do there unless I have some sort of personal stake in it.
If the other party has done something horrendously wrong, hurtful, or harmful, and you're pointing it out, and you don't feel inclined to be nice, or you're pretty sure that "being nice" would detract from the point that hey, this is NOT AT ALL OK, sure. Again, not my place to say, particularly if I've no stake in the matter.
I'm also not in the camp that declares that any disagreement or criticism is meanness. There are mean ways to do it, but the act of saying "This is not correct" is not inherently mean. Saying "You used "it's" instead of "its" in paragraph 3" is a statement of fact (if, in fact, there is this error there) that's phrased neutrally, although a lot of mean-or-not-mean depends on context. If all you ever say to this person is pointing out their typographical errors, you might be being mean. If 20 other people have already pointed out that error, you're very probably being mean. If you feel like you're being mean when you do it, you're being mean.
It's also okay to disagree without pounding your opponent into the ground, depending on the circumstances. It's not always about winning.
Are you being mean because all your friends are? Check yourself. There are more productive group activities. Even if you are being mean in private.
Are you being mean because the other party is unfit to defend themselves? Check yourself. That's the definition of a bully.
If the other party has achieved some measure of fame, success, or other variety of notoriety, and you are of the opinion that they should not have this, and you have set out to be mean to them for the purpose of taking them down a peg or two, or similar? This? Actually not okay. Bonus not-okay points if you included something like "take that [slur] down a peg or two". Double bonus for "uppity".
Perhaps it's that you don't believe that someone who isn't actually all that should be getting that much attention when there's [insert more worthy item here] that people could be paying attention to? Go ahead, promote that other thing to your heart's content.
Perhaps you think there are problems with this person and/or their work that cannot and should not be ignored? Go ahead, point them out.
Perhaps they were mean to you? Excluded you when you thought you should have been included? Had the temerity to have fun with their friends and tell the whole world how much fun they had? Own it. Figure out for yourself whether saying so makes you sound like a person with a reasonable problem with them or a whiny child.
But if the heart of the reason why you're justifying being mean to someone is that they're too successful, check yourself. Refine your reasons before you flame away.
(Have I myself failed on this front before? I am very sure I have. Let's start with elementary school and carry on from there. So this is as much a reminder to myself of my own ethical stance and ideal behavior as it is a statement to the world.)