Whatever your definition, feminism is an ideoloy. A belief system. Not an incontrovertible, material reality.
Therefore, the fact that someone who belongs to the oppressor class cannot simutaneously be a member of the oppressed class on the same axis of oppression is irrelevant in deciding whether a member of the oppressor class can adopt a belief system that fights for the liberation of the oppressed class.
Take the anti-slavery movement. By the definition many here hold, no one could ever be an abolitionist who is not or has not been enslaved. This is demonstrably untrue, as we know from history.
It is logical therefore to conclude that anyone can be a feminist who subscribes to and acts on the belief system called feminism. I think however, that the problem with this question, and why it is so hotly contested is that
a) the definition of feminism is not clear cut and for part of the feminist movement it has changed beyond recognition.
To me it means the liberation of females from the patriarchy. Like the liberation of humans from slavery, this can only be achieved by destroying that which oppresses us - the patriarchy.
Whether they're aware of it or not, for most libfems for instance, the fight for the equality of women as a sex has now become the equality of women as a gender.
And Libfems already start from a position of achieving equality from within the patriarchy, thereby capitulating from the outset to the system that oppresses us. The implications of marrying the latter position to the former are dire, as we know and the seeming predominance of this kind of feminism is, I would argue, what led us here, to the impending loss of a vital part of our rights.
Radfems, or as I call them feminists seek the liberation of females from the patriarchy by destroying the patriarchy. That does not mean revolution (although that would be faster); we can achieve this aim by dismantling patriarchal structures.
If you want to be a feminist then in my view, you must recognise and understand the structures and mechanics of the oppression of females and you must undertake steps to play your part in dismantling them, however small.
Any man who does this, is a feminist in my view (like the father of Malala for instance).
But and this is probably the more important reason for the disagreements:
b) The trouble is that most of the men who call themselves feminists are none of the sort.
If you look closer at their view, most take a libfem stance of working within the system (that serves them so very well after all) and advocating for equality, not equity - patting themselves on the back if the company they're running pays female staff the same wages for the same work but ignoring the fact that their C-suite consists entirely of men.
And the guy at home, who totally believes his wife should have equal rights, but when she finally starts to work after sacrificing her career, won't be taking over any of her duties (like staying at home to look after a sick child) or work fewer hours so she can devote herself to her own career, is not a feminist.
He might share the belief in the liberation of females, even understand the patriarchial structures, how they oppress women and why they must be destroyed, but he's not willing to make any personal sacrifices to do something to address the consequences of this oppression.
So can men be feminists - yes
Are the men who claim to be feminists, really feminists - unlikely