I find such a request irrational.
Any of those things really does provide Bayesian evidence the relevant groups will have lower status in a community. There are tradeoffs between making a place pleasant for various people and the ability to talk about various subjects. Even if strict general epistemic norms are applied (which would throw out most articles from political sites anyway), relaxing taboos to allow even clinical discussion signals unusual priorities. If avoiding offense or increasing participation of a group is a very high priority, then people will only bring up such evidence if they are relevant to some other very important need.
You seem to be in an argument about where to set the tradeoff seem to be making a claim about where to set the tradeoff, and I wouldn't say positions become necessarily "irrational" across a wide range.
There are tradeoffs between making a place pleasant for various people and the ability to talk about various subjects.
For instance: Making it pleasant for fundamentalist Christians makes it hard to talk about biology, because in order to make fundamentalist Christians comfortable you have to lie about biology. Making it pleasant for white-supremacists probably implies not having any informed conversations about the experiences of nonwhite people, since the nonwhite people are not likely to stick around to defend their very existence against the white-su...
Summary: Current social psychology research is probably on average compromised by political bias leftward. Conservative researchers are likely discriminated against in at least this field. More importantly papers and research that does not fit a liberal perspective faces greater barriers and burdens.
An article in the online publication inside higher ed on a survey on anti-conservative bias among social psychologists.
The link above is worth following. The problems that arise remind me of the situation with academic and our own ethics in light of this paper.
I can't help but think that self-assessments are probably too generous. For predictive power of how an individual behaves when the behaviour in question is undesirable, I'm more likely to take their estimate of how "colleagues" behave than their estimate of how they personally do.
This shouldn't be surprising to hear since to quote CharlieSheen: "we even have LW posters who have in academia personally experienced discrimination and harassment because of their right wing politics."
While I can see Lammers' point that this as disturbing from a fairness perspective to people grinding their way through academia and should serve as warning for right wing LessWrong readers working through the system, I find the issue of how this our heavy reliance on academia for our map of reality might lead to us inheriting such distortions of the map of reality much more concerning. Overall in light of this if a widely accepted conclusion from social psychology favours a "right wing" perspective it is more likely to be correct than if no such biases against such perspectives existed. Conclusions that favour "left wing" perspective are also somewhat less likely to be true than if no such biases existed. We should update accordingly.
I also think there are reasons to think we may have similar problems on this site.