I don’t think this is really a question of psychology, more philosophy or self-improvement. It also depends on whether your personal definition of cynicism is traditional or contemporary.
That being said, those two things are not mutually exclusive. You can vocalize your opinions, in any situation, without putting others down or being off-putting. A big part of it is just knowing your audience and learning tact.
Remember that being cynical isn’t the same thing as being right or an insurance of critical thinking. Assume you might be wrong, you certainly are about some things because we all are. Tactfully and respectfully bring up your viewpoints without disparaging anyone, it’s just as another possibility to ponder. It is arrogant to assume you presenting your opinion is you educating others of the truth and probably where most modern “cynics” draw the annoyance of others. Remember you aren’t in parliament or debate club and you aren’t changing the world or convincing anyone of anything within one conversation. You are stating your views and if the wisdom of your words resonates then it will have an impact after a time. If not, at least you put your views out in the zeitgeist. Changing minds is a slow process. Don’t let others’ stupidity or stubbornness phase you, just laugh it off internally. Smile every so often, even online, to remind yourself you are conversing with a fellow human. Learn how to ask Socratic questions. Read Plato’s Republic. Read the Tao Te Ching. Read Machiavelli’s The Prince.
My best advice is don’t discuss things to change the mind of the person you are talking to, chances are they aren’t going to budge. Speak in a way that would convince others silently listening or reading along of the wisdom of your views. Be an ambassador of kind wisdom, not a soldier of viewpoints.
Only share your cynical thoughts when it’s helpful to do so
