Haidt glosses over the political left's justified suspicion of supposedly scientific narratives that reassure incumbent elites that their power and privilege are part of the natural order. At the same time, it's certainly true that politically-sensitive questions -- Are there inherent differences between the sexes, or between distinguishable popululations of humans? What are the origins of sexual preference? -- are a minefield for would-be objective investigators, even if their motives are beyond reproach (as if that could ever be established beyond doubt). Maybe that's as it should be; I don't know. I am not enough of a knee-jerk leftist to assume that arguments and framings of reality that happen to be congenial to leftists are ipso facto correct. To that extent, I'm in sympathy with Haidt. I would be drummed out of any "serious" left-wing organization as quickly as I'd be drummed out of any "serious" right-wing organization.I've been in loosely default-left academic settings and among activists all my life -- and as you say there is no question that viewpoints across the political spectrum provide hooks for intolerant assholes and zealots to hang their hats on -- but depending a bit on what you mean by "serious," the knee-jerk liberal characterization seems to me to largely a matter of folk mythology.
I mean, would-be theocratic religionists often pretend they are being crucified simply by being confronted by the existence of atheists and agnostics and secularists, however nonjudgmental and cheerful and welcoming the latter are trying to be, you know? And so, too, some assholes wail about "political correctness!" and "thought policing!" just because they discover themselves in settings where the norms are not defined by white middle class heteronormativity or even when people different from them report that their prospects are dimmed or even simply that their feelings are hurt when issues are framed from that normative vantage.
Again, I agree that there are self-righteous folks and conversation-stoppers to be found in every ideological precinct. But my experience is that once someone reveals themselves to be open to discussion the progressive polycultural left really tends to give folks the benefit of the doubt and to treat folks as generally open to change of conviction to the better through argument. Such conviviality seems to me an entailment of the left's animating premises, not that this would stop your common or garden variety jerk particularly.
Too many complaints of left humorlessness and intolerance to the contrary seem to me to arise out of the efforts of boors to crash what are in effect private parties among marginal folks looking for safe spaces to relax in or among wonks with highly specialized jargons not really ready for prime time. Or, again, too often they really do seem to amount to expressions of incumbent outrage at having pet pieties challenged.
The long and the short of it is, I really do think you are little likely to be drummed out of any serious lefty assemblage worthy of the name when someone as prickly as me finds welcome in such places -- and did even back when I was much more of an oaf and ignoramus than I have managed to become later in life.
As for the specific issues you raise, it seems to me that sexual orientation arises from historically and situationally contingent articulations of material propensities. Some flower seeds germinate quite visibly different morphologies depending on the altitude at which they are planted. The reason these issues are so fraught tends to be the result of moral and political judgments that inevitably freight what are often framed as neutral observations. Even if one makes a defensible case for a more exhaustively genetic account of sexual orientation than I would advocate myself, it seems to me important to find a way to account for the experience of sexuality as importantly unchosen by straight folks as much as by queer ones, as well as to account for the extreme variation of sexuality (butch/femme, top/bottom, eroticization of morphological differences and so on) that seem conspicuously underdetermined by genetics and yet quite as foundational in their individuating sexed/gendered force. People who are marginalized in their differences also tend to be more sensitive to the ways in which animus is articulated in what bills itself as objective description -- as when physical differences are described not as differences but as deficiencies, excesses, imbalances, and so on.
As for differences among "the races" or "the sexes" (even pretending for a moment that these terms account, as they do not in fact, for quite material realities like the existence of mixed-race, transsexual and intersex people that scramble their reassuring typologies fatally) it seems to me that much that gets excoriated as anti-scientific denialism among reactionary evopsycho douchenozzles claiming to be champions of science is really a highly pro-science insistence on more careful language and specificity of observation. When bigots speak of "race" in the delineation of observable traits the populations subsumed by the category tend to be different from one another -- "raced" observations of susceptibility to certain diseases, "raced" observations about drug sentencing, "raced" observations on performance on objective tests (usually indifferent to differences in preparation for the tests), "raced" observations about wealth distribution and so on tend to refer to loosely overlapping populations woven together in public discourse by what remains a conspicuously contingent sociocultural category of race as a space of identification/dis-identification. These things matter, and should also matter to folks who claim to respect scientific rigor.
Again, rationales for irrational patriarchal or racist prejudices that peddle themselves as matters of respect for science often indulge in sleights of hand over the domain of applicability to which questions are properly put. Even if one were to demonstrate a difference in general IQ differentiating teenaged Canadian women from teenaged Canadian men or Pacific Islanders from Subharan Africans or whatever, if one is in charge of a public university or presides over defense attorneys, say, then one has made a commitment to provide equal access to public resources to the served community or equal access before the law whatever the differences among citizens may be. In such debates it will be political questions of responsibility that matter even if the objective status of the overgeneralizations is the distraction the reactionaries want to focus on. If sooper-genius Larry Summers decides he has sound evopsycho evidence that women in general are less good at math than men are he cannot justify giving less Harvard scholarship money and departmental support to women on the basis of the belief that such money will be "wasted" otherwise since his institution serves the whole community. This is quite apart from the fact that even if such a generalization were true judgments on its basis would irrationally benefit men of less than the average male math intelligence over women of more than the average female math intelligence (don't you feel your intelligence dropping just talking this way in the first place?) even on his own premises. And all this is quite apart in turn from the fact that the premises themselves are the most flabbergasting false sexist idiocy imaginable in any case.
And, again, I do not agree that the left is more hesitant to address sensitive questions than the right is -- I think too much of the right just want their insensitivity to be treated as a virtue when it isn't, which is not at all the same thing.