It's totally immersion breaking for me. I get really deep into my roleplaying, and when they do something out of character it makes me pull back in frustration.
Honestly - I've pretty much given up trying to role-play in Bioware games since DAO. It just isn't possible, at least not for me.
I've only very recently started the ME series after getting a decent deal on the Trilogy. I knew going in that Shepard was going to be Shepard, and had no expectations of being able to role-play the character. I choose something on the wheel, she does whatever she does, sometimes gets some paragon or renegade points, and I move on. In that way, it has been an enjoyable action-adventure romp, an interactive fiction of sorts, but is in no way a role-playing experience for me. From that perspective, I'm starting to understand why people don't want to deal with inventories, stats, etc. - mechanics that have long served as abstractions in role-playing - because what you are ultimately doing is driving a character through some grand adventure, and a lot of the elements that have traditionally been part and parcel of role-playing might not serve this other form of entertainment media.
That said, Shepard is a whole lot more straightforward and easy to understand than Hawke ever was. Shepard has a background, specific roles as an Alliance Officer, CO of the Normandy, Spectre, and clearly defined objectives. Hawke is a civilian going through the motions - anytime I ever tried to define any sort of goals, agenda, or motives for the character, the game (or the character herself) would do something to contradict them - lol.
I wonder if part of the problem is that the Inquisitor exists in some space between being as defined as Shepard and as loosely defined as Hawke? The Inquisitor does have a background and ultimate goal set by the game, but leaves a lot of characteristics, personal motives, etc. open to player definition while the tools provided for the player to express the character are confounding?
I'm bummed that Bioware is no longer making games that I can use as role-playing platforms. There are certainly other developers who are, but none of them have the depth of NPC characterizations, personal relationship building, romance, etc., that Bioware offers up on a silver platter.
In any case, I hope you can find a way to ease the frustration and enjoy the game. 