It's fine to say that sexist hiring practices are wrong because relevant skills can be assessed directly, and so using sex alone as a proxy for something else like physical strength or intelligence would serve only to reinforce the biases of whoever's doing the hiring. But if you say such hiring is wrong because there are no statistically significant differences between men and women for such-and-such characteristic, then you may have dug yourself into a hole. In general, we probably haven't done enough research into that characteristic for anyone to be able to say for sure, and so you've left yourself open to losing the entire basis of your argument should evidence arise that shows there is in fact a difference.
Relying too much on arguments like that also leads to lots of political objections to basic scientific research. Not ethical objections, mind you. Nothing wrong with saying that perhaps we should take more consideration for the well-being of test subjects and lab animals, for instance. I mean more along the lines of someone on the right objecting to research showing that, say, increased sexual activity in adolescence leads to healthier offspring later in life, or something like that. Or someone on the left objecting to research that shows objectively that newborn boys and girls, absent any social influences, really do differ on average in their levels of aggression or interest in mechanical things or whatever.
Early promiscuity is probably bad for a number of other reasons which outweigh healthy offspring later, and rigidly prescribed gender roles probably cause plenty of serious problems that outweigh any slight benefit of encouraging a small inborn natural tendency. So it should be the promiscuity and prescriptive gender roles themselves that are objected to. Not the research or the researchers involved in discovering more information about the human condition.