The thing about genderqueer, gender non-conforming, and even to an extent so-called "binary" trans people is that we all have the "right" to mysteries considered unique to men or women respectively. There are people who disagree based on the idea that if we have access to both sets of mysteries we are in effect "taking" more than we're entitled to, appropriating things that we haven't experience or reject as experiences. Which of the sets of mysteries we're supposedly "appropriating" depends on how trans-friendly the person making that case believes themselves to be... there's a noxious theme, for instance, of trans-excluding "feminist" traditions believing trans women don't belong in women's mysteries work, while there are also those who don't believe, say, a trans man should be anywhere near those same mysteries.
What doesn't occur to people is this: A trans or especially genderqueer person who feels called to both sets of those mysteries is called to them for a reason. This is at the heart of why so many cultures viewed third gender people as valuable, special, and powerful. In short, we ourselves are aspects of both, so why not utilize both?
(Related note: If you are trans and absolutely do not want to be associated with the mysteries of your assigned sex, that is absolutely your right as well. Hell, there are cis people who hate those mysteries, too.)
If you are not in the category of folks who have a strong aversion to participating in them, I'm giving you permission right now. If you're a trans person who feels called to either set of mysteries, or both sets of mysteries, even if it's not your lived gender, you're empowered to study that. Are you entitled to, say, join a women's coven as a trans man? No. Are you entitled to every single gendered ritual that exists in every culture ever? No. But you can certainly read women's mysteries books. You can read men's mysteries books. And the same goes if you're a trans woman.
A blanket content warning: A lot of women's mysteries books are pretty openly transphobic, by which I mean they explicitly talk about trans women (and men, but mostly women) in a vile, inappropriate way. If you want one that isn't, they do exist ("Jailbreaking the Goddess" is a pretty good one). Secondary non-warning note: I have yet to encounter a men's mysteries book that excluded trans men, and a good number of them are actively inclusive.
Feeling anxiety about whether or not you've "earned" it? Women's mysteries and men's mysteries aren't something cis people earn, it's a birthright. A trans person by virtue of living as trans in a transphobic world has "earned" it through intense perseverance more than the average cis person has.
"But what if I don't have the 'parts' or cycles these mysteries honor?" Cis people--especially cis women, who generally acknowledge more biological mysteries than men do--have come up with alternatives for these for themselves as a coping mechanism for things like hysterectomies and infertility for years, and those who exclude trans people from these concepts are deliberately being transphobic. These concepts include things like spiritual wombs, following moon cycles, and simulating a natural cycle through birth control (the latter being something trans women regularly do) are appropriate ways to experience women's mysteries and genderqueer mysteries if you do not have the same cycles as an average cis woman. And plenty of the milestones celebrated by women's mysteries--pregnancy, in particular--are increasingly eschewed by cis women. If childfree cis women are welcome to honor their wombspaces, so are you.
Didn't go through the same milestones at the same time as cis people? Don't sweat it. Role-based mysteries are so archetypal that most cis people don't technically qualify either, if literalness were necessary. How many men honor some sort of hunter figure--hunter being seen as some primordial male mysteries role--who have never even shot a bow and arrow let alone killed an animal? Seriously, there's a reason those weird "Sacred Hunt" rituals are so popular, it's because cis people wind up not doing these things, either.
It's absurd that we would box ourselves into one set of mysteries when we are by nature supposed to be powerful. We are the children of Agdistis, of Set, of Hermaphrodite, of Dionysos.
These mysteries belong to you as much as everyone else. It's OK to own that.