Yes, this is a big deal for me and always has been. I am a former Kemetic Orthodox priest, and currently generally pagan; I follow some "shamanic" practices (not to get too much into a discussion of the use and misues of the term) and occasionally explore Faerie work.
"Two-spirit" describes me best of all the terminology -- I have no claim to Native American cultural heritage but it is still a near perfect match. I'd encountered the "ergi" concept before and that also fits. (My spouse is a Lokean and I've learned a bit about Him and Odin through her.) I've also read about a Sufi group where the holy men consider themselves female in the presence of God.
As do I. I'm really only on the feminine side in a religious or magical context or in certain kinds of dreams. In daily life I have a somewhat weak sense of gender, not identifying much with manhood or womanhood, but sort of a dark gray purple in terms of the enby pride flag.
I present as male, am equally okay with "he" or "they", don't have much of a comfort zone with interdressing (*), and I don't have a physical sense of dysphoria.
I dreamed once of a young pair of twins -- one male, one female -- living on the edge of civilization, guided by a particular spirit object; as the dream progressed I found that I was both twins.
In another set of dreams there was a powerful god nearby whose brilliance forced me to look away (something I've experienced in ritual as well) and I had the sudden distinct feeling that I was female
because He was so close by.
In a series of other dreams I've met a mysterious smiling woman, and gotten the sense over time that she was actually me.
While thinking about this thread this morning, I found myself with the urge to buy or make a long skirt for dancing (a colorful circle skirt and/or something with a lot of flying ribbons) and use that in my magical practice. (I did used to wear a galabaya in Kemetic Orthodox practice, though in its culture it isn't a gendered garment.) Like I said, normally I'm not comfortable with wearing womens' clothing; but I feel like in the context of worship and magic it would suit me well. At least according to some internet sources, some cultures' shamans used that sort of clothing to represent flying. I've always had an affinity with the wind more so than other elements so maybe that's where this is coming from.
(*) -- wearing or shopping for womens' clothing generally makes me feel ridiculous and self-conscious. While I have some drive to express my gender identity outwardly, I don't want to be read as being in drag or as trying to pass for female. Because it's a difficult situation and I feel so weird about it I generally keep my signs very subtle or hidden -- colorful over-the-knee-socks with my jeans, jewelry under my shirt, maybe painted toenails that nobody ever sees. It's enough to appease myself without feeling awkward.
(I did wear a women's button-down shirt to my job interview though because it was the classiest one I had. It was pretty subtle and I don't think anyone noticed which side it buttoned on. I got the job and nobody said anything at any rate.)