Lunatic's Bizarre Rules of Fair Play (which I wind up breaking myself sometimes, but I try to keep)
Keep in mind, this is my view on the universe. I'm not necessarily recommending that these are good rules for everybody, but here's a peek inside my brain.
If you hate a person who is not a public figure, keep the hate part private or otherwise secured. It's sufficiently uncouth to hate without really really good cause that you want to think twice before declaring that in public. Depending on your particular skill at handling stuff like this and the cultural background, you might be able to state the fact that the two of you do not get along while in public. Mistrust is an iffier zone, and can lead to personal attack territory very fast. Unless you actually want to start something with them, keep the personal attacks locked down.
If you hate a public figure, while it's tacky to go on and on about how much you hate them, personally, in public, I suppose you can do that, but I still think it's really tacky. Try to confine it to dislike/mistrust. Some public figures really have earned hate, and I don't want to say anything that could be interpreted as endorsing things like hate ministries or people being racist fuckheads or other sorts of ways people are hateful failbuckets, but ... try not to hate on the petty stuff, eh?
If you hate a public figure for their looks ... sheesh, people, why? There's a big difference, to me, between "I hate $CELEBRITY; they're ugly" and "I don't much care for $CELEBRITY's looks; couldn't they have picked a more attractive person for $JOB?" I can deal with "I resent that $CELEBRITY, who is widely regarded as hot, is far less attractive than I am, and I don't get that kind of recognition!" -- but I can't read your mind to realize that you're envious of the benefits $CELEBRITY is getting out of a below-your-standard looks package, not just loathing of how they look.
And then there's "I don't think $CELEBRITY meets the appearance requirements for $ROLE..." and that's a casting quibble, which is a completely different beast.
I don't at all see the sense in hating a public figure for their looks when their looks are not part of anything that has anything to do with their job.
I also separate general resentment of the concept and implementation of an appearance-focused society from individual personal dislikes. I loathe the fact that people of very little other sorts of redeeming value can get by on trading on their looks while people of competence can get passed up. And fashion. God. Fashion. Why not just encourage girls to take arsenic for their complexion and put belladonna drops in their eyes to dilate them? For fuck's sake.
If you and someone else have formed a mutual loathing society, for crying the fuck out loud, please leave any mutual friends out of it. That's not to say that they shouldn't know -- they should know. But it's bad form to try to drag them in.
Some phrasings, and my thoughts:
"$EVENT, and I felt that was unconscionably rude, and now I loathe the very sight of them," is fine. It's likely to make them uncomfortable, since they will be caught in the middle, but they may have a need to know how you feel, if not a need to hear every little detail of your loathing in subsequent conversations.
"I don't know why you still associate with that rat bastard after $EVENT; if you were really my friend you'd drop them like a hot potato!!" is not so much with the fine. Would you like to guarantee that your friend is likely to not choose you? Please continue in that vein.
"Ever since $EVENT, I've been trying to sever any and all connections with them, and could you please tell me if you are planning to continue to associate with them. I really would like to continue to associate with you, but unfortunately cutting ties with them is my first priority," is a regrettable situation, but fine phrasing. Of course it'll cause drama -- no one likes to hear that they're less important than your (perhaps justified) loathing of someone -- but it's perhaps one of the least hurtful and least demanding ways that the particular situation could be explained. (And of course there's the perpetual argument of not wanting to start drama by letting people know that you're leaving them, and why you're leaving them. But if you do try to explain, that's one way.)
I'm Ravenclaw. We do phrasing, some of us. The word-geeks work on nuance.
It's not necessary to explain why, of course; some things really shouldn't be shared. But if friends that you share with them are going to get involved, it's fair play to let them know that there's something up, even if you can't give them the details.
If you're writing a bad review of entertainment, are you doing so to honestly help the creator improve, or doing so for your own entertainment? If to help the creator improve, by all means let them know or make it public. If you're doing so for entertainment, there's no need to a) let them know, or b) make any public link between the review and the bad entertainment itself. (Though some things do require context.)
If you're entertaining yourself at the expense of someone else's failed attempt at entertainment, consider: did they create it for their own entertainment (incidentally sharing it with the public), did they create it for the entertainment of the public as a hobby, or did they create it for the entertainment of the public professionally?
If they're professional, snark away; there are some nationally released movies that never should have been.
If they're a hobbyist aiming at the public, they could probably stand to know that they fell short of whatever mark, but there's no need to share with them the cruel details of your snark. Know the difference between critique and snark. Snark is usually funnier than critique; critique usually gives some credit for a genuine attempt and gives specific points of improvement phrased at least neutrally, or helpfully if possible.
If they created it for themselves and left it public, keep your snark in an arena where they shouldn't be able to find it, and don't poke them unless you have constructive feedback (even if it is just "You could really use another pair of eyes running over your spelling before it goes out in public," because gods know a lot of writing, fanfic and otherwise, could use that. Or at least a goddamned spell checker).