> I only have one example of why;
I think there are plenty of reasons why. But if someone's arguments are good, it does not matter who they are. If someone doesn't want the limelight, that is fine. I mean look here, my handle isn't my name. Though I wouldn't call it exactly anonymous/secret either.
> it's more difficult for people to engage with a nuanced opinion.
It is more difficult, but recognize that a common fallacy is "my opinion is nuanced, and yours is simple."
Which you experience here
> ascribed a set of beliefs to me which I did not hold
There's a tactic that I've found that has a decent success rate. The key comes down to that language is messy and that it is difficult to capture someone's nuanced position quickly. Your brain fills in missing information and does the best it can to figure out what the other person is trying to say. There's three parts to communication: what you mean, what you say, and what is heard. So if you don't know that these things are different and that your brain is filling in stuff (that this goes both ways) you're going to have a difficult time communicating, especially in a divided time with extra tribalism. This is essentially why divide and rule/conquer tactics work, because we are actually unable to communicate with one another.
So if you recognize this and when it is happening, stop the conversation. Divert and establish a foundation. "Hey, I think we're having some miscommunication. When you mean x do you mean f(x) or g(x)?" Then you listen carefully and don't interrupt (I bet they will develop nuance, if not they will add more later). At some point it is natural for you to speak again and address the misunderstanding and explain your nuanced point. If they start interrupting calmly explain "Hey, I have a nuanced point and I do not feel like I'm being able to finish an idea and thus we won't be on the same page and both be frustrated. I would like to finish the idea first." Because you listened to them carefully before and gave them time they now feel obliged to do this. The whole conversation has slowed down but everyone is now speaking the same language and hostility is gone. The pace will naturally pick back up.
As an example I was talking with my roommate the other night and we were getting heated. I had to apply this method and basically say "Hey, we're throwing in too many things at once. I don't feel like I can finish an idea before I address a specific issue. It is impossible to for me to talk about 30 different and nuanced subjects at once." He did slow down. Mind you he also said "Well that's how <insert nationality> people speak, I guess we can just handle that many topics." Don't let that kind of thing phase you, because if you want to have a real conversation you have the be the better person. This is probably the hardest part (let someone make themselves the asshole and let them realize it, you don't always have to point it out).
tldr: disengage, slow down, reestablish definitions, reengage.
But if you want to fight, win, or get one up on the other person, these techniques will not help you accomplish that.