There is a LOT of evidence here. This is heavily studied. No, feminists didn't just make this up out of whole cloth.
It did used to be fairly common to pay women less than men for exactly the same work, even controlling for seniority, commute, hours, etc.
THAT HAS BEEN OUTLAWED IN THE UNITED STATES SINCE 1963.
Of course making something illegal doesn't make it go away, but there have been many law suits, a lot of time in court, billions of dollars in claims payouts etc.
There are STILL a limited number of cases, mostly caused by ineptness (nobody checked) and women not having any idea what their compatriots are earning.
One of the suggested law changes was simply that salaries are posted. Clearly there's a lot to that. Some employees are more valuable than others and you're willing to pay more for them, but you really don't want to argue with every employee paid less why. That is not reasonable. Unless the reason you're paying somebody more is because they are male, white, Christian or really any demographic, in which case they have every right to be pi$$ed off.
Unfortunately, "pay gap" is measured by most feminists in ways that do not take into account different working habits between men and women. Women are more likely to need flex time, will statistically take longer off for children, are more likely to use company supplied benefits etc. These things become statistically predictable overhead that companies are NOT ALLOWED to use in compensation calculations though they certainly come off the bottom line.
Moreover, women are FAR more likely to make quality of life choice job decisions that bring in less salary than men are. Women are more likely to get into disciplines that historically don't pay well because they find those jobs satisfying (e.g. social work).
The highest paid jobs have been STEM and management jobs. STEM jobs are overwhelmingly held by male employees despite companies deliberately hiring women preferentially simply because far fewer women want those jobs. Upper management is both stressful and risky, things women tend to find less interesting than men.
This doesn't mean they couldn't do the job. It means they DON'T WANT to do the job.
With this push back, you end up asking feminists "Do you think women should be forced to make career decisions more on the basis of salary than they currently do?"
About the most coherent reply I've seen comes down to "some should, and more men should be taking quality of life over salary".
At some point, it becomes clear they are looking for men and women to GET the same things out of life misunderstanding that that only happens (and is stable) when they WANT the same things out of life.
VERY few women, for instance, are willing to have a baby and then completely hand over care to her husband. There are far more men who simply treat it as a foregone conclusion that they will be second fiddle in their children's lives.
Feminists generally are incredibly good at discarding data they believe hurts their case and simultaneously telling people what they should want. After awhile, the rest of us get tired of it.
WAS a feminist until a bit more than 4 years ago. When I started asking pointed questions, it was only a matter of time before they kicked me out.