Here are two statements that are worth bringing together:
"The anti-knowledge and anti-science sentiments expressed repeatedly during the U.S. presidential election threaten the very foundations of our society."
"The pronoun discussion is not simply about grammar or gender – it's about re-examining the very beliefs upon which our society is based."
The first is from "An open letter from women of science", which, according to Jessica Kirkpatrick at the Women in Astronomy blog, was written by "a group of women scientists who have been working in Washington as AAAS science fellows". It's sort of a vague affiliation, but I take it seriously because it is being promoted by the CSWA. The second is from an opinion piece for the CBC by Julian Paquette weighing in on the Jordan Peterson controversy.
I will presume that Paquette and the "500 Women" are natural allies in the current iteration of the culture wars. But the ideological contradiction is here quite glaring and very common on the Left. Depending on the issue, the ideologues are prepared to declare either that "the very foundations of our society" are threatened or that "the very beliefs upon which our society is based" must be questioned. I think it's fair to say that this ambivalence is itself foundational for "progressive" politics.
One way to resolve the contradiction is to assume that they are talking about the foundations, not of our society, but their society. That is, they are talking about the basis of the ongoing progress towards the utopia they imagine. And that utopia is indeed "science based", if you will. As the "Open Letter" put it: "Science is foundational in a progressive society, fuels innovation, and touches the lives of every person on this planet." What about a "conservative" society? we might ask. Perhaps innovation is there fueled by something like human ingenuity and initiative, and perhaps the state is there constitutionally restrained from building institutions that, somewhat creepily, propose to "touch the lives of every person on the planet".
These foundations need, precisely, to be conserved, not implemented after traditional beliefs about what people are and how they can most happily live together have been "re-examined"—a word that is almost certainly a euphemism for "overturned". I have to say that, given the state of science (and the science of the state, if you will) these days, I understand the anti-science sentiment. Many pro-science people seem to the think that science is simply epistemic authority: an institution that has the power to tell you what to think and to believe. I like to think of science as a protected space of free thought and inquiry—not a place where I'm forced to examine my beliefs, but where I'm allowed to.