My beliefs hold a theory on this. ^.^;
The soul retains your whole mental existence, so it is definitely gendered. Since gender seems to be part of some of our more core parts of identity, it is likewise part of the soul to hold it as an important aspect of practiced identity. If how you act at one time is a persona your personality uses ---your soul takes your identity, gender and all, as just one persona of itself, in a way, even if it is the only persona it holds. The spirit, a channeled instance of the soul dealing with reality, is more purely gendered according to your mind rather than simply hosting its presence. It is also sex-ed according to your gendered identity. (The soul, on the other hand, does not have a sex due to its structure.)
Although it doesn't seem to be asked, I wanna go ahead and remark towards the concept of consciousness: I know there's some beliefs out there that transsexualism, or even multiple/all kinds of ->-bleeped-<-s come from spiritual aspects, such as reincarnation from a mismatched gender, a soul that develops itself inaccurately to the body, etc. --My beliefs consider on this that your physical consciousness holds your personality as well as your soul and spirit, because of how exactly mind<->spirit<->soul relate with each other. The mind holds your transsexualism full-stop, but holds it as that you are a transsexual rather than that your mind is of your true gender.
Finally, I feel there's a separate aspect of the "essence" which is somewhat soul-like but very temporary state. It has a sex in terms of that it hosts the body structure of a sex, but does not hold a gender because for what parts of the mind it hosts, they effectively aren't active. It furthermore only indirectly has a sex exactly like the soul indirectly has the gender, because of its structural design. The essence directly reflects your physical sex at all times.
So in short~ Five parts of a person: Essence, Body, Mind, Soul, Spirit.
Essence - sexless, simulates current sex, absolutely genderless.
Body - <Everything as put in practice>
Mind - Combines aspects of sex and gender and is a transgender accordingly.
Spirit - Sex is ultimately where gender identity lies as true, gender always is as gender identity and thus of the sex.
Soul - Sexless, genderless, simulates gender.