I think it's impossible to talk about "male privilege" as trans people without first discussing and deconstructing the fact that this term was coined by and for cis feminists who have baked in assumptions about what "male" and "female" are. Cis feminists did not have trans people in mind while developing the language we use for these discussions. We need to push these discussions further, now.
What I mean is - "male" is a loaded term in terms of gender & sex in a similar way to "female". When people use it in cis society, they're usually referring to the traditional wolffian body type - penis, testes, no boobs, no uterus. Many discussions of gendered privilege are based on what different cis peoples' bodies can do, especially in terms of reproductive labour. But of course, trans and intersex people do not follow the sexed and gendered norms and cannot be discussed with this same framework without somehow misgendering or miscategorising ourselves. "Male" and "female" are themselves very difficult terms for just about every type of trans person.
One type of "male privilege" often discussed by cis feminists is that cis women often have to go around in their day to day lives menstruating, in incredible pain, while bleeding, and unable to discuss this in most professional settings due to the sensitivity of and potential backlash from the men they work with. This is a real, tangible problem that is upheld by both the bodies of the people involved and society's period-fear at large. It is also held up by the patriarchy at large, keeping cis men in charge and afraid to discuss or be made aware of menstrual issues. The ability to not ever think about menstruation is part of structural male privilege.
My problem with this all swings in when we look at trans people under this lens. You can't clear-cut this kind of thing. Can trans men have male privilege? Sure, a trans man - especially a white one, as the patriarchy thrives off of white supremacy - can probably assimilate well enough into Male Culture to attain some of those trappings of structural privilege. But he can still never talk about being on his period [a feminist issue] around cis men without punishment. He is still in more physical pain than his cis male counterparts [a feminist issue]. He still has to spend money on period products [a feminist issue - and what does his pay gap look like next to his cis counterparts? entirely situationally dependant] and more time doing laundry after he ruins his favourite pajamas [I'm just sad about my jammies]. And he will never be able to attain the structural male privilege of never thinking about periods in his life, unless he undergoes medical care to stop his periods - which still does not erase all lived experience of menstruation, experience of being shamed for menstruation, or sympathy for people who menstruate. Meanwhile, there are trans women who develop obvious menstrual symptoms - intense pain, emotional swings - and are told by people of all kinds that they're hysterical, or that they're lying bitches just looking for attention. Their pain is ignored routinely in the same way cis womens' pain is, except it is seen as even less legitimate because they are trans women. They are allowed to speak about it even less, because there is no telling who in the room will say "lol, trans women don't get periods". This is blatant bioessentialist misogyny [and an obvious feminist issue!!]. The trans women are certainly not benefiting from "male privilege" here (unless you count not having to buy menstrual products, but I think that's a topic for nuanced discussion between individuals and not something to make a blanket statement about on tumblr dot com). And none of us regardless of what kind of trans we are (lol) get adequate reproductive or sexual healthcare.
The period thing is just one example because I'm on my period right now. I don't really have a conclusion other than that contemporary discussion of patriarchy is often built off of discussion of sexism, and based in biological sex. There are ways to discuss the impact of patriarchy (and of these body-based disprivileges under a patriarchal society) without being transphobic, intersexist, and bioessentialist, but it does require recognising the kyriarchy of it all.
Which I guess means it's time for terms definition. Kyriarchy is a basic intersectional framework for looking at systems of power and oppression.
A kyriarchy is an intersectional and interlocking set of hierarchies, all of which do their part to privilege some and oppress and subjugate people of certain identity groups.
As an example, men might oppress women as a whole in the kyriarchal approach, but it’s also possible a white woman could oppress a Black man. Similarly, a Black woman with no disabilities might have more privilege than a Black woman with disabilities.
The benefit of viewing things in kyriarchal terms mainly lies in revealing the complexity of how oppressive systems operate—a person might find themselves both subjugated and privileged simultaneously at different levels of the kyriarchy.
This definition of the word was coined by feminist scholar Elisabeth Schüssler Fiorenza in 1992, who considered oppression to be far more complex than the frameworks of sexism and patriarchy that feminism had been building on at the time. Wikipedia says "it is an intersectional extension of the idea of patriarchy beyond gender", which is exactly what trans & queer people need to be embracing as a framework.
I really think more discussions of "who has xyz privilege" would benefit from understanding that we live in a Kyriarchy, and that how each person is seen and given privilege in society is entirely situational and based on many interwoven factors that play off each other in sometimes unexpected ways.
That's all for today, peace and love, go research feminism and care for the people around you without abandon <3