I spent significant time traveling and working in Ukraine and Russia from 2003 to 2011 and I can confirm that for many women the outlook isn’t great. That said, my impression is that young professionals are trying hard to break away from the stereotype: they drink far less, and they have more egalitarian attitudes, than previously. Blue-collar citizens, however, remain more or less stuck in the bad old ways.
My sense is that when Russian-speaking women seek Western partners, mostly they’re doing so out of a genuine desire to forge a real and lasting relationship rather than simply looking for a visa and a way to a materially better life. Unfortunately some of those who arrive in the USA are swayed by the “get rich quick, the only thing that matters here is money” attitude that’s dominant across the 50 States, and over time this can cause significant problems.
And if the American man isn’t very educated or informed, he can quickly begin to feel inferior as Russian speakers usually have a wider world view and know far more about global affairs than insular Americans whose media tells them practically nothing of events outside the USA. Russians also tend to have a stronger sense of family, which can be an issue when a woman is 11,000 kilometers and 10 hours of time zone distant from those she loves.
As for language, while Russian is more difficult to learn than European languages like French, Italian, Spanish, German etc. it is much easier than Finnish or Hungarian or Thai or Chinese. The grammar is fascinating, the pronunciation of words is very regular, and it’s really easy to learn the Cyrillic alphabet. Any man considering looking for a partner in the Russian-speaking world should really make a serious effort to learn Russian because if you can’t communicate with her family and friends, that’s going to be a problem down the road. Because you will be part of the family, and families talk together.