coming from a woman doesn't preclude it being sexism - sexism is a structural rather than individual problem, and women are just as immersed in the overall sexist culture as men are.
However, it reinforces a society's underlying sexism, racism, etc. So you often have to work against capitalism to fight other oppressions. And vice-versa.
Some forms of trade will always exist, but there's a fine line between trade, monetary systems, free markets, mercantile capitalism and modern (AKA industrial) capitalism. Which too many people seem to confuse as one.
And to answer your original question, of course capitalism isn't sexist, it's a broad economic system. However a capitalist system can suffer from sexist tendencies when the rules (laws, regulations, culture, society, etc.) governing it push it that way, the same any economic system can.
In this sense no nation has any real power over capitalism itself. If they enact regulations to try and reduce sexism within their borders they run the risk of reducing their constituent corporations' ability to compete on the global stage.
It's not that easy. States are not coherent actors. People are watching out for themselves first, for their corporations and states etc second or third.
Somewhat more optimistic, different countries have different rules. The power of arbitrate to even force the same level of taxation seems pretty low. (And forcing the same level of sexism seems even harder.)
Capitalist economies are carefully implemented by states; refusal to implement these artificial things puts your country at risk of terrorism by militant capitalist states. You may like Graeber's _Debt: The First 5000 Years_ for a useful perspective.
Maybe, but to argue thew other side, we have a god-free universe filed with people who wonder if they've joined the one true church.
I find that it is difficult to get shit done with that mindset though, so I live my life as though I did not believe it.
A classic world of colliding billiard balls is much harder to predict.
That relies on some emotionally intuitive notion of "responsible" which I cannot bootstrap from what I know of the universe. That is why "free will" is foma to me. Rationally I do not believe it to exist because I cannot define it rationally (not only do I find myself unable to do it, I believe that it is not possible).