I've been doing some period writing lately, and just as much lately, I am running into sexism. That is, I am running into both the sexism of the period and the sexism in myself.
The sexism of a period shows up in three ways: genre sexism, trope sexism, and real-life sexism.
Genre sexism is part of the stories that you try to write. If you are going to write about men going on an adventure, then you have the problem that you have a novel full of men, and possibly some women. This sexism is not due to someone having a secret agenda, but merely because so many adventure books were written by men, for men. Just by writing in a genre and a time period, you gain that structure. That doesn't mean that the structure is inescapable, but by seeking to escape from the structure, you also lose something of the genre.
The next sort of sexism is Trope sexism. What should your women be like? What are their personalities? How should they act within the story? Not only are there modern tropes about what women should be like, there are period tropes as well. These are clearly sexist. You can forego these tropes, as many period stories did, but by skipping them, you lose more of the period feel. However, that doesn't escape you from all tropes. Your male characters are, most likely full of male trope, so it gets odd to have a properly fleshed out female character while the male characters are full of trope.
Finally, we have the kicker of real-life sexism of the period. This I am most uncomfortable removing, because that's like putting wallpaper over the past and pretending that it wasn't what it was. To me, that is the worst disservice possible. I could, of course, as many genres do. I could be very fair to everyone, but the price would be blandness. I can skip overt sexism where the entire point of the story is to assert the white male's dominion over the earth, but I can't skip the cultural norms sexism.
Add all these types up, and avoid all these types, and you can easily wind up with stories that don't feel like the correct era.
So, what do you do? That's where I scratch my head.