As a general point I think some people misunderstand what some people mean by the terms "racism" or "sexism". Sometimes, those terms refer to specific acts in which someone does something explicitly racist or sexist. So if I tell women that they are biologically hardwired to be homemakers while men are hardwired to be breadwinners, and therefore it's not only natural but right that men earn more than women, then that's sexist. That's just me being sexist, holding sexist views, and saying a sexist thing. But sometimes, "sexism", "racism", etc refer to something systemic: it refers to a consequence of seemingly natural and entirely explainable socioeconomic circumstances that are the fault of nobody in particular, but that benefit a set group to the detriment of another group. So if I take my previous example, sometimes, we use the word "sexism" to refer to the system that produced the illiberal or unjust result of women systematically earning less than men, rather than any specific act of sexism or sexist viewpoint.
I think a lot of the time, people mistake accusations of the latter against "the system", and people take it as the former -- against them personally. I think we need to be aware of the distinction, and make it very clear what we mean. And when we hear that we have said something sexist or racist, we need to be clear about what that means, too. It might not mean what we think it means, as they say.
This isn't something that happens a whole lot, but it happens more often than I see acknowledged. It sometimes leads to misunderstandings.