I think there's roughly two good strategies for having conversations with people.
The first is actually speaking your mind freely once you get to know someone even a bit, including all the politically incorrect things.
As a somewhat tame example, I think the British Empire did more good than any other nation in history and was overwhelmingly a force for good in humanity. However, people mostly hear about their bad deeds, but don't hear about all the suicide cults, assassin's organizations, human sacrificing religions, and so on, and so on, that they ended. People also take for granted all the hygiene, infrastructure, rule of law, scientific method, and so on that they propagated.
I'll point this out, even though it upsets some people. It's honest and not politically correct (but true!).
There's another strategy, which is to suss out what the person you're speaking to thinks, and try to converse on common ground and without being offensive. Done correctly, this actually means being liked by a wider group of people and not offending as many people... and this isn't so bad, really. Most people will lionize speaking up in theory, but react really hostile in practice if you say, for instance, that you think universal suffrage is a terrible way to choose a government.
Anyways, you can guess which camp I fall into most of the time, but the second one is good. The second way is much more open to making connections with everyone. Seriously, almost everyone has something of value that you could share with them, but if you say that British imperialism was a huge net gain for the world and universal suffrage was a huge net loss, then you're going to miss some connections you could make. If instead you talked on what's relevant to a person and you, you'd have a lot more consistently pleasant and good conversations.
What you probably ought to avoid is doing something that's in neither camp. Most people don't speak their mind, but also don't really care about finding out what's important to whoever they're talking with... so conversation drifts to just... nonsense, I guess. Really trite, smalltalk junk. That's no good.
Option 1 - Speak up, honestly, even if it's controversial. This gets you into lots of fascinating discussions, makes the people who like you really like and admire you, but creates enemies and people who despise you as well.
Option 2 - Find out what whoever you're talking to cares about; talk about that. Also produces lots of interesting conversations - you don't get to cover some interesting topics, but you make up for it by being able to learn from many, many different kinds of people. Most people will like you, but you get less extremely strong supporters than Option 1.