The argument for women being allowed to vote and women being allowed to work in factories, along with being paid the same (which is still ongoing) was via highly organized spreading of word and demonstrations. Articles were written, flyers passed out, petitions written, discussions were had all over. These were all considered at the time, uppity issues that was more or less bullshit that "we" the american people should focus on core values such as family instead.

To be frank, women's sufferage really was formulized in 1848 arguably, and then took until 1920 to actually happen. During that time, there was similar discussion to what we're having now. The idea of basic values have changed because of cultural discussion, over the course of decades.

I would argue that equality of sexualities has increasingly become another core value, with the debate of such happening over similar amounts of time. The discussion of course is still ongoing in this field and I'm eager to see what will happen in the future.

I think we may be talking past each other a bit. To me cultural relativism is the claim that we have NO grounds for saying one set of values is superior to another. Women's suffrage is the very opposite, It's a set of values people felt passionately about and fought for. And now it's embedded in western culture. And we have good reason to believe that cultures that embrace it produces more flourishing and 'happier' people.

You should read Thomas Sowell's "A conflict of visions". It's short and really great. It's about why people group themselves into the political left and right, and why those sides disagree.

One of the points he makes is that the left and right don't agree on what the words "equality" or "fairness" mean. Right wing people tend to focus on equality of process. Left wing people tend to focus on equality of outcome.

That is, a conservative will tend to say "is the hiring process fair? yes? then if 90% of the jobs go to men, there's no problem". Whereas on the political left, they may say "if 90% of the jobs go to men then by definition the hiring process is not fair, and we should find a Solution, like by setting quotas". Right-wingers will tend to reject direct intervention like that, as they don't trust in human ability to intervene without causing unexpected and undesirable side effects.