I'm not seeing why that's necessary. Historically, patriarchy is pretty obvious. Women were forced into specific roles for thousands of years, and that was clearly still happening during the lives of many people now in the workforce.

So I'm comfortable just taking women at their word when they say they're still experiencing problems. I don't need to carefully measure the exact relative degrees of shittiness. Worst case, I will listen to them and solve some problems that turn out to be for everybody.

But if you're merely curious, I'd recommend reading some of the articles where trans people talk about sexism from both sides. E.g.: https://newrepublic.com/article/119239/transgender-people-ca...