There's an apocryphal Christian story, that I heard or read long ago -- where somebody asks someone else (possibly a Buddhist):
- Have you ever thought of becoming a Christian?
... to which the person replies:
If you mean a good Christian, like your Christ -- I don't have the courage.
But if you mean being a bad Christian, like you -- I wouldn't want to be!
If you want to be persuasive (about the benefits and/or truths of Buddhism) perhaps it's important to be a good Buddhist.
I don't want to criticise but "ending up in heated debates about the existence of God" doesn't sound attractive or persuasive to me.
I'm particularly afraid of someone's thinking, "if being a Buddhist means being like you, I wouldn't want to be!"
I once tried to explain Buddhism (not in a "confrontational" way) -- see How to explain what Buddhism is? -- and I don't think I was very successful.
Still I hope I learned from that, that there are many different aspects of Buddhism: and different aspects appeal to or make sense to different people.
The Buddha was especially skilled at knowing different people and speaking accordingly.
It may be that the topics of God, Soul, and Self are especially important to you -- for what it's worth or for example, I don't see that as the most important doctrine.
A friend once told me a bit about communication theory, saying that when people choose a topic of conversation, then talking about what's far away (distant) is less intimate than what's close (here); that what's in the past or future is less intimate than what's now; and that talking about people we don't know, and/or talking about friends, is less intimate than talking about ourselves.
It seems to me that talking about "God" is very distant. Perhaps it's too easy to argue about something you can't see!
If you want to talk about Buddhism maybe it's better to consider aspects of Dharma like Ehipassiko, perhaps like the Kalama sutta.
Five more things.
One is that I tend to assume "good faith".
My parents professed Christianity when I was young. I don't think they were doing that in order to deceive me.
I assume they had some reason[s] for their belief[s] and that the words they spoke had some meaning[s] to them, even if those words didn't wholly make "real" sense to me.
So if I were going to engage in a conversation about God and Soul and so on, I think my participation ought to include my being interested in finding out or understanding what those words mean to someone, and why they use them and so on.1
Conversely, if I'm not interested in doing that, then it's maybe not a topic of conversation I should engage in.
The second is that (when I was young and they were trying to indoctrinate me) I was willing to believe all kinds of doctrines. Or if not believe, at least not dispute. "So, God wants us to love our neighbour as ourself? Well sure, why not. Good doctrine, more or less. And God loves us? That's nice to know, thanks for saying so. And there's a resurrection and an afterlife? Well, OK: if you say so." There was one bit of doctrine though that I couldn't manage. The way it was taught at that time was, "The Church has a monopoly on the Truth: what the Church teaches is true, and everything/everyone else (including every other religion) is wrong." And I thought, that bit of doctrine was just too much: "So, 'the Annunciation', OK, 'the Trinity, Transubstantiation, Purgatory, Heaven' ... whatever, OK: if you say so. But 'everyone else is wrong'? That's incredible! Impossible!" And I think that maybe Buddhism too warns against being a sectarian who argues in this way ("This alone is true") about the dhamma.
The third is that I guess (if you'll excuse my saying so) that your "heated debates" are motivated by some form of conceit, specifically comparing yourself to others: "I'm Buddhist and they're not. My being Buddhist means I know the Dhamma, whereas they are living in ignorance." That's maybe not something you want to perpetuate (even when the debate is whether 'self' is an illusion).
Fourth, if you are arguing online that's maybe even less sensible/effective than face-to-face (xkcd).
Fifth, IMO the "ideologies which totally contradict Buddhist beliefs" are for example the ideologies which involve killing -- or lying, and so on. If you understand that kind of doctrine to be the "bottom line", you might decide most people are agreeable or "very civilized".
1Maybe you can see this sort of attitude here, i.e. I like to assume that I'm at least a little ignorant about another person's views.