Personally? I prefer to be able to play a female character (sometimes nonbinary characters), though choice games are actually the only games where gender choice for me is a knock out criteria. I think it’s for two reasons: 1. The number of games which present (the choice) for a female character as protagonist is still pretty limited depending on the genre (And sometimes the advertisng of a game doesn’t even mention that chosing the gender of the protagonist is possible), so I would most likely miss out a bunch of games and 2. When it’s not a choice game the game mechanic often plays an as important role if not more important as the narrative (Just look at the number of games with terrible story that still manage to be funny because the story is not the main part of the game if we are honest).
Choice games on the other hand are somewhat build on story and immersion of the player, so it makes sense when at least for me that gender choice is more important for those games (And I also feel somewhat spoiled because games that don’t allow me to play my prefered gender are here quite the minority 
)
But on the other hand I also wouldn’t want a writer that wants to write a specific “gendered” story to change that because of pressure from the outside even when they are very opposed to it from a story stance out. Some stories work only with emphasize of gender and a gender locked protagonist. Even when people say “hey you just could change the way your game world is build” in the end that wouldn’t be the story the writer wants to tell.
And in the worst case you would end up with a rashly/unmotivated added choice that the writer hadn’t fun with (because it felt like betrayal on the own story) and the players neither (because the choice leads to consequensces that aren’t thought through and make no sense with the world building), though the worst case probably would be the writer abandon their project because of the frustration. (I have seen both cases play out).
If you say you want to write a story that only would work with a preset gender than do it. If it’s writen in an appealing way people still will play it. Just look at Guenevere and Guns/Sabres of Infinity which have a huge fanbase.
An alternative when you want to add a gender choice but don’t want to write a completely different game also could be to just swamp the gender roles at whole like Broadsides and Pendragon Rising do it. That could be a compromise when possible and if you feel comfortable with it. However I don’t know if you may want to use the game world you are creating in other games with different stories, that wouldn’t need a locked gender protagonist, too; in that case for the sake of consitency that option may also be less than optimal.