I think a lot of people have already touched on what I was going to say.
Basically, how something is presented shapes your perception of the overall narrative flow. Even if multiple-choice options don't radically alter the direction of the story, the answers you're giving can still alter your perception of the main character, or the people around them. So your overall experience of the story will be slightly different (and you'll have more of a feeling of shaping your own destiny, even if it's mostly an illusion).
For example, let's say I'm in a game/story where the plot absolutely needs me to follow one friend (Bob) into a haunted forest to try and find/save another friend (Alice), and I'm given options like this:
a) Sure it's dangerous, but Alice might need help!
b) It's way too dangerous! I don't want to go... but Bob's going, and I can't let him go alone, right?
c) Damn it, I really don't want to go in there. But Bob's going, and it might be even more dangerous to try and go back the way we came alone... guess I'm stuck.
d) Ehh, yolo!
While from a mechanical perspective all four of those options are entirely identical (you and Bob are going to go into the forest), from a narrative perspective they all differ. The first tells me that the main character is loyal to their friends and wants to proactively save Alice. The second option makes the MC more hesitant, but still loyal enough to Bob (or just afraid of being called a coward) to not want to abandon him. The third option implies the MC is just too afraid to simply say no, and the fourth option implies the MC is either utterly fearless, utterly stupid, or extremely impulsive. My impression of just what sort of character the MC is is going to be different in all of those cases.
Another example of this sort of thing is from Knights of the Old Republic, when you're training to be a Jedi. When you're speaking to the Jedi Council, at one point in a conversation you're given the option to say something along the lines of "I promise I'll be good" or "I promise I'll be good [Lie]". It doesn't matter which one you choose - both lead to the exact same reply, and the game doesn't track your answer in any way for future conversations - but YOU as the player know the difference. Your perception of your character has now changed - either you are sincere in your intention to walk the noble path and use your powers for good, or you are already plotting to use your powers for evil and are deceiving these deluded fools who were stupid enough to trust you. One choice has allowed me to look at that main character in two very different ways.
Third example - in Fallout: New Vegas, you can have a conversation with one of your companions where she mentions fish. This being a post-apocalyptic world full of radioactive pollution, she pauses and asks if you know what fish are. You're given dialogue options to tell her you know what fish are, to act confused like you have no idea what a fish is, or to just sort of brusquely wave it off like it doesn't matter. None of those choices matter in any way - they don't really change anything in-game other than a few lines of dialogue in response. But which you choose tells you more about your character's past (maybe you're from a region that's healthy enough to have fish, maybe you're from a Vault and have never seen them, maybe you're well-read and have heard of fish from books, maybe you have no idea what fish are but are self-conscious enough to avoid the question, etc).
The important thing is to make sure whatever flavor choices you allow don't conflict with other things in the story. If I'm given a choice to say that I don't like someone, don't have the MC later blurt out how much they love that character without any player input. If I'm given the choice to enter the haunted forest enthusiastically, don't have the MC shout later that he never wanted to come in the first place. If I'm given the option to tell someone I'm into dudes and have never been with a girl, don't have my ex-girlfriend from college show up later and talk about all the sex we used to have. Future dialogue essentially needs to be neutral enough to make sense regardless of which previous options you've chosen.
I think those sorts of "pseudo-choices" are only really bad when the player feels like the choices don't matter at all. Like if you give me the option in-game to throw a knife at the bad guy, shoot him with a gun, or run away, don't have the knife and gun options both result in "You miss" and force me to run away anyway. That feels like a bait-and-switch and can frustrate players, making it even more obvious that they have no agency, which just makes choices feel a bit insulting/pointless. A choice should make it feel like there's absolutely a difference between the two options, even if its only in the relative short-term.
Telltale games are pretty notorious for this. Some people will complain that no matter what choices you always wind up following the same general plot and ending up in the same place anyway, but the real appeal of Telltale games was more about how those choices shaped the path you took to get to that ending. You still have the feeling of some agency over how a character reacts, and the power to shape their personality to some degree (even if its only in how you perceive them rather than how they're presented).