it’s just that equality feels like prosecution to those who have traditionally lived charmed lives
I cannot speak for "that country", assuming you mean the US, as I don't live there. That said, I think people don't have actual past lives as a reference. If my grandfather or father lived in a different world, this can at most create expectations, but cannot be really generating a feeling of prosecution, because the current one is the only life I have actually lived and I know.
Then there is another issue, which is that in reality there are a lot of factors that determine whether you are born "in third base". Gender, historically, has been one of them, but it's far from being a guarantee. However, the political discourse often flattens this issue and makes it almost two-dimensional. If you are a white man, you are privileged, period. Fact is, there are tons of white man that are absolutely not privileged, and are also victim of an unequal and oppressive society. These people are substantially alienated because their voice is simply not represented anywhere.
My leftist interpretation is that some of the egalitarian discourse (feminism, LGBT rights etc.) has been to some extent swallowed by the status quo, and lost a lot of the revolutionary potential it had, becoming more focused on individual perception and rights, rather than on systemic issues that therefore could capture also the dynamics of a white man being also oppressed, even if from a different angle.
In other words, if feminism is purely focused on battles of women as a group of individuals, and not as part of a system that oppresses them within a wider mechanism, then oppressed people that don't strictly belong to that category have a much harder time to see in women a reflection of their own oppression.
Basically, a realization such as:
We’re all the same to them now, and will all be exploited as such.
was true already decades (centuries) ago, and that's why lots of feminist battles were linked to socialism and leftist ideologies. This is nothing new, really, and forcing to read the current issues only from the racial perspective or only from the gender perspective (etc.) makes it much harder to build solidarity between groups who are instead left to fight battles within the system, without a perspective or a struggle to move past it.