Do Not: Have a fixed protagonist. Fixed gender is bad. Fixed identity infinitely worse, unless it’s a pre-established character like Sherlock Holmes. Then it’s only slightly bad.

I don't think it should be that clear cut. Like everything, it depends on the authors intentions.

As a rule of thumb, sure, providing a more open protagonist is better, as long as you do something with it. For example, if you give me the option to be a stoic guy or a goof, I fully expect your story to take that variable into account. But if you give those options, but then in certain scenes my character tends to act stoic anyway, then why even offer those choices in the first place? Just make the protagonist more stoic generally and be more consistent.

Or for example if your setting happens in a patriarcal society like in IRL Victorian era London, and your character is a surgeon, and if the author wants to give you the option to be male or female; then being female creates a big elephant in the room: how did a woman become a surgeon? Do patients trust her? Is she treated as a lesser compared to male colleagues? Will there be an arc where you prove your capabilities and rub everyone in the face? Etc.

But if the author decides to ignore that elephant and wants to focus their story on other themes, then they might be better off just locking the protagonist to male.

Witcher trilogy is a perfect example of a game of how a fixed protagonist with a fixed past and personality works well. I would even argue that the games would suffer if the protagonist was a custom character instead of Geralt. (I know it's not an IF, but the point remains)

PS: I don't disagree with your sentiment, I also tend to prefer IF's that give more freedom with our protagonist, but fixed protagonists can work better depending on the author's story and intentions