I've been watching some stuff on some, hrm, less-than-savory YouTube channels and reading some stuff on equally-unsavory subreddits, and what they say is that granting further rights to women and letting women have positions of power have contributed to the fall of historic civilizations, like, say, Rome. They say Rome fell because they let women take charge. Is this true? I know Rome fell because of many reasons, but is that a part of it? They say it might happen again.
Can you cite some specific sources that these groups and people use to make their claims? And if these groups and people do not cite sources I would not give their claims any validation or even a second thought. And, if they can disclose sources, check who has written them, when, for what possible purpose, and does the conventions present in the sources correspond with other conventions of the specific culture and time-period of the source?
Correlation does not equal causality. I have yet to encounter any source saying that gender equality caused the downfall of the Roman empire or any other empires. If anything it could be that it was a sign that the great empires were losing their grip in general, making rebellions of oppressed groups more likely.
Just because two events coencide, even multiple times, it does not suddenly equate that they have anything to do with each other. I bet you could make a graph that says the increase of immigrants to Norway shows a similar tendency to an increase of vegans in Canada, but that does not mean immigration to Norway causes veganism in Canada. I think you get my point. There are three kinds of lies: White lies, damn lies and statistics. You can use the last thing to prove pretty much anything you want as long as you find the right statistics.