I’m going to answer this one, because I struggled for a while myself with the contradiction of trans women and male privilege. The solution, though you may not want to hear it, is to read more and don’t confine your reading to cis authors.
Trans women may have internalised elements of toxic masculinity or patriarchy throughout their upbringing, but they do not benefit from cis male privilege. A cis man may demonstrate his male identity in any way he pleases and society accepts it. A trans woman cannot. A cis man will not face discrimination in the workplace based on how he demonstrates his maleness. A trans woman will. A cis woman may also find her ability to express her female identity restricted. As such, cis women and trans women share a common cause in which both can benefit from the shared spaces offered by equality activism.
A far greater issue is the silencing of trans men’s voices when cis women who don’t support transpeople’s right to exist and trans women come into conflict. Perhaps you might turn your attention to problematising this issue, rather than problematising how “woke” culture tries to support oppressed minorities. Support is good, oppression is bad. That’s the long short of it.