This is something that predates my active dive into PbPs,
and something that I learned to accept, but the biggest immersion-breaker would be non-diegetic game-mechanical choices - what the Alexandrian calls
dissociative mechanics. Note that I'm using this term in the specific technical sense, relating to player agency that affects the narrative directly without being mediated by character agency. I'm making this clarification pre-emptively because too many times I got retorts like 'but to me so-and-so does not
feel dissociative', and my comment was never about how mechanics feel on their own, but rather about their structures of causal chains / 'control schemes'.
[ +- ] Example
Diegetic examples: Spending Willpower in Storyteller/WoD is a fully diegetic action: the player decides the character should try harder, the character tries harder and the character's effort is improved, but gets more mentally exhausted. Also, Willpower Points are meaningfully interactable for characters - e.g. characters can learn the Meditation Secondary Skill (IIRC from the Vampire Player's Guide or something), which allows spending time meditating to restore Willpower faster. Similarly, Health Levels (the ST analogue of HP) represent the character being wounded, and can be interacted with by diagnosis and medicine.
Non-diegetic examples: spending Fate Points in many systems is something that the player chooses to do, but it often does not in any way shape or form involve the character making a decision - e.g. when an Event Compel in FATE Core happens and the GM says 'unfortunately, stormtroopers show up in Mos Eisley in search for the droids' and the player decides 'yeah, stormtroopers show up in Mos Eisley, and we get the FP for the Compel' or 'nope, I am going to spend a FP to say that no, stormtroopers do not show up in Mos Eisley'. The character is completely outside of the decision loop. Similarly, Stress in FATE Core is often openly described as 'plot armour', not a tangible state of the character (though the more diegetic-friendly GMs and players often wave hands vaguely in the direction of more tangible signs of Stress happening).
Now, I do appreciate the benefits gained from such non-diegetic mechanics, and am willing to continue with the sacrifice of immersion of these benefits, and still I think it's the most glaring immersion-break I had to get used to.