Well, this idea has been explored in fanfiction before, but I mostly see Asami turning into an Equalist in those, which doesn’t make a whole lot of sense to me, lol.
Taking her becoming an Equalist out of the equation, it wouldn’t change too much I think, unless Yasuko took Hiroshi’s place in the story and became an Equalist, then I don’t think much would have changed. Of course we know jack-diddly-do-da about Yasuko, so no one can say for sure.
But, if we’re talking about neither Asami nor Yasuko becoming Equalists, then honestly, I’m not sure. It would certainly affect Asami’s story within the show, that’s for sure, since her whole story pretty much revolved around her relationship with her father. It’s quite possible that she would have only become a minor character and not part of Team Avatar (and thus no Korrasami, oh what a sad day that would be).
(Sorry if it sounds a little weird and I don’t make any sense, I’m really tired right now.)