I think the main reason there is so much opposition is what happens when it does. Then there is no reason to change the laws/policies (because they don't override how humans are built). That means there is no reason for the careers of politicians and activists and no money for the initiatives to fix it. So it becomes a self-fulfilling prophecy.
In practice, of course, biology explains a large portion of differences between humans, both where it pertains to gender, and where it pertains to race.
There are a few "forbidden truths" for them:
1) That there are in fact biological reasons for some aspects of a gender gap.
2) More general there are reasons for discrimination in certain limited cases (it used to be the case that the law had specific exceptions for diversity regulations. The big example given was "no cripples in the emergency response team in the fire department" (I think you can imagine why). That was a valid discriminatory demand that could be put in job applications)
3) There can be no differences in the source population (because ... well if you calculate it out specifically, then the Bay Area is not racist in hiring at all. But wait ! Why are there soooo few blacks working for the Bay Area tech companies ? Why so many Asians ? Well ... those values are very close to what you'd expect them to be if well-established (but heavily denied) racial differences in intelligence are taking into account and one assumes that when silicon valley invites 10 people to compete for a job, they hire the smartest)
So in order to have "equality", defined as "distribution in the winners of competitions is the same as the distribution of participants" you can't have even tiny differences at all in the population beyond their proportion of the population, otherwise that'll never happen. Unfortunately there's another problem here (see next point)
Of course the whole reason different races exist is to have them be different. I mean from the perspective of evolution, which while it isn't a conscious entity, does have both the means to change humans and a reason to do so (a goal to achieve). This means races/genders don't just differ in skin color, they differ in anything. Obviously the skin is one important difference, but it is just one component of profound differences in energy regulation of the body, which affects nearly everything relating to energy use in the body, which ... even affects brain size. Specifically one big difference between races is how much energy gets dedicated to body temperature maintenance (cooling and warming are different systems, so that's 2 separate things), digestion, muscles/movement, and ... yes ... how much energy gets dedicated to thinking, and even the balance between cortex and neocortex. And if it favors the cortex, that is just not going to help out your chess game. It even affects how big you are on average (of course bigger = everything requires more energy, because the human body is not that different from a robot. Fortunately bigger requires exponentially more energy, so the differences there can't be that big)
4) The effect of average differences on competitions. Specifically, say you have group 1 and group 2, and they compete. Let's assume N(100, 10) distribution. Let's say group 1 has a x% higher average, how often would a one-on-one competition between a member of group 1 and group 2 end in favor of the member of group 1 ? Let's call that value y.
for x = 1%, odds of group 1 winning = 53.01%
for x = 2%, odds of group 1 winning = 55.57%
for x = 5%, odds of group 1 winning = 64.04%
for x = 10%, odds of group 1 winning = 76.08%
for x = 20%, odds of group 1 winning = 92.19%
And if you have repeated competitions (you only advance to the next round if you win round 1, and there's N rounds) ... it gets pretty bad pretty rapidly.
So unfortunately competition amplifies small differences in averages. Although this is to be expected, this is why natural selection works.