There are many kinds of immersion. Some are crucial for me, some I don't care for and some I see as problematic.
I can't imagine having fun playing without emotional engagement. If I don't care about the characters and what they do, I'd be better off playing a board game.
It is possible to pull me out of this kind of immersion by negating the meaning of my character's choices or destroying things about the characters and the game world I care about.
I immerse in the story we create through play. I like emotionally charged situations, I like unexpected plot twists, I like characters being played to the hilt, even when it puts them in trouble.
I identify with my characters, but I never "become" my character, perceiving things as they do and fully sharing their emotions. I play my characters aiming to create interesting situations, not to "do what my character would do". This kind of immersion I don't care for.
And when I read about immersing so deeply that one stops thinking about the rules of the game and other people at the table, I see it as a pathology. If you stop thinking about the real people playing with you, the way you communicate with them, the feelings it creates - there's nothing stopping you from behaving like an ass while believing yourself to be a great player or GM. I've been there and don't want to ever return.