Honestly, it’s hard to make a prediction. There’s no real data I’ve seen one way or the other.My children are mixed heritage, as my wife is Japanese. Which means my children are directly in the line of fire of something like Shadows Over Innsmouth and they don't have the luxury of being blissfully ignorant of that since it's pretty freaking blatant. So, fine, they decide to start playing D&D and pick up the 5e PHB, turn to the page listing the Inspirational Reading - not a bibliography, but including a direct quote from Gary Gygax about how important it is to read to become inspired to play D&D.
So, they go out to the local library and pick up a handful of these, including Shadows over Innsmouth because, let's be honest, it's readily available in many libraries and, because "Lovecraftian" is a pretty common description given a positive meaning, it would make sense to read it. It's certainly part of The Complete Works which is listed in the 5e PHB.
They read the story and get to the end. Now, what do you think is the more likely reaction:
A) Oh, well, that's just a product of the time, but, this hobby that I'd like to get into doesn't really support that despite directly telling me that this is an inspiration for the game
or
B) Oh look. It's another racist bigot in a long line of racist bigots being defended (Oh, it's just a product of the time, we don't really think that way anymore) by another bunch of racist bigots and promoted by yet another bigot.
I mean, virtually every American who tried the hobby in the first decade or so who isn’t a white male has had to deal with a wide variety of bigotry in the games themselves as well as the genre fiction that inspired them.
And yet, some of us still play the games and read the fiction.