When I was growing up, there was a saying that conservatives are people who believe in genetics, but not evolution, while liberals believe the opposite. This wasn't an entirely fair generalization, but did capture some significant truths.
This interesting New Yorker article focuses on the left-wing side of the equation. Many on the left are reluctant to acknowledge the social impact of genetics, for fear it could be used to justify inequality, racism, and so on.
One aspect that the article doesn't touch on is that the left actually has an obvious alternative approach to dealing with genetics, pioneered by such thinkers as John Rawls, Ronald Dworkin, and other "luck egalitarians": if economic and social inequalities are in large part caused by genetic endowments, that strengthens the case for redistributing the wealth generated thereby. From this perspective, people whose wealth is largely the product of their genetic endowment haven't "earned" their riches. They don't have any special merit; they are just lucky beneficiaries of the genetic lottery. Thus, there is every reason to redistribute some or all of that wealth to the less fortunate. To the extent most of the latter are in that position in large part because they "lost" the genetic lottery, they don't deserve their poverty any more than the rich deserve their wealth. On this view, the more genetic endowments are a cause of inequality, the stronger the case for various traditional left-wing policies! Far from weakening the case for the left, genetic determinism can actually strengthen it.
I don't buy "luck egalitarian" moral theory, myself. I also think luck egalitarianism overrates the role of luck and underrates that of institutions and incentives. But, then again, I'm not a left-winger. And many who are not on the left will at least acknowledge that advantages due to luck/circumstances of birth are less deserved than those caused by hard work or virtue.