> You can get every case, every article, and every syllable correct

For articles, natives say sentences with wrong articles in them too. Seldomly because they don't know it (still happens), but because they change what they want to say mid-sentence. Cases are always a fight between the pendants and people who don't care.

Plain incorrect grammar will of course be noticeable, but grammar isn't everything.

That's not what I meant, and I too switch words mid-sentence.

And even if my word choice, register, or what have you is wrong, I don't understand the attitude. Because when they make mistakes in English I don't even comment.

I think this really depends on the people you surround yourself with. I'm a native German and I get "complaints" that I do not correct enough, because I just try to have a conversation instead of being a language tutor.