I've found people who do this to be incredibly toxic, mostly because more often than not the opposite viewpoint has been disproved by a body of scientific literature with which the "devil's advocate" is entirely unfamiliar.

In that case, playing the contrarian is nothing more than trolling.

When doing this, make sure the opposite viewpoint is at least as valid as the one you're arguing against.

There are just no arguments for homeopathy or Young Earth Creationism. It's a natural reaction to get angry when someone argues in clearly illogical ways and is not open to rational discussion. (it's natural not because "rational" is somehow "better", but because of the helplessness of the situation).

Not every "idea" is valuable to be heard. That said, you don't state what topics you argue.

I do the same. I have found that both conservatives and liberals get angry. But by far, the harshest are liberals, in my experience.

I get irritated pretty quickly if I think someone is playing devils advocate straight. If I'm having a discussion with a person, I don't want to have a discussion with an inverted caricature of my views.

I think the difference is obedience (to whatever world view exuding from whatever real or imagined authority figures) and drawing self worth (or, more realistically, constant background fear) from that, and being grounded as a person and having opinions about things which one is free to re-inspect and change without losing anything. It doesn't matter so much what people think but why they think it, or rather, if they think or parrot it.