There's more to it, imo.

If you breakdown the statistics, you'll see that women who are married to men tend to be conservative and in alignment with their husbands. It's single women that have significantly different beliefs.

Immigrants tend to come already married and/or they bring a wife/gf from their home country, eventually. This leads to the women among non-whites often being in alignment with their husbands. I imagine if you tracked 2nd and 3rd generation immigrant women, you'd start to see a trend where in general the women and men deviated in beliefs because you'd start to see more single women in the 2nd and 3rd generation immigrants.

Furthermore, immigrants don't tend to vote the correct people in power because immigrants don't understand the politics in the domestic countries. Leftists are good at lip-services and immigrants tend to believe them so in general immigrants tend to be leftists, simply because immigrants do not understand things and are often less intelligent than domestic whites. That means the immigrant men and women will often vote the same way even if the men should be voting a different way due to a lack of understanding and how the immigrants are easier to trick politically.

The problem isn't that white men and women are being specifically targeted to have opposing beliefs. The problem is that feminism itself which leads to increased single white women causes a divide. Immigrants have less exposure to feminism when they first arrive but the longer the stay the more these immigrants start to align to the feminism of the domestic white women.

Feminism is the root problem. Women that get married young to a man have no issues. It's the single "strong independent" women who are a problem.