Are feminists (who subscribe to the view) right to claim that all men are necessarily sexist? Perhaps it makes sense to limit the scope of the claim to a particular country, say within the UK. Presumably the sexism of men in few examples of matriarchal societies, if indeed they are sexist, would be different from the sexism we're familiar with.
As a man, I would not care to insist that I am not sexist in various ways. My morality is egalitarian but it is no doubt at odds with my attitudes and behaviour. That applies to gender just as it applies to other ways we distinguish sets of people (or subjects of moral concern).
The problem I have with the assertion is that it seems to take gender (or sex for the transphobic flavours of feminism) as the essential dividing line between people.
Aren't there all sorts of predicates that group people into different sets, some more privileged than others? 'Born-in-the-UK' vs. 'Born-in-Malawi'; 'disabled' vs. 'fit'; 'socially anxious' vs. 'charismatic'. In many cases, the privilege conferred by belonging to one of these groups is far greater than that conferred by maleness.
Perhaps the idea is that gender interactions play such a fundamental role in our lives, and are buttressed by social institutions, that males unavoidably adopt gender prejudice in a way that doesn't apply in other cases. I suspect that similar arguments could be made for other cases. If so, it will be difficult to defend the assertion without expanding it into a broader claim.
They could just bite the bullet. They could claim that everyone in any privileged group with the relevant social reinforcements is necessarily prejudiced against the underprivileged group. That seems implausible.