There should be an option for the PC to present as androgynous, rather than strictly masculine or feminine. It should be difficult, unlikely to achieve by accident, and would probably confuse the shit out of everyone you meet.
Perhaps it'd be a different story for NPCs (named or otherwise) who know what your genitals look like, though I can imagine some of them asking for your pronouns anyway in likely-not-very-woke ways.
Game mechanic idea: Fallen Angel!PC working for Angel!Jordan themself, as a sort of assistant: an Acolyte. Your one and only objective? Keep Jordan pure.
Jordan has been tainted by a powerful elkspawn, and it is up to you to help mitigate that taint before it has a chance to spread within them (or, worse, to others). Luckily, the high priest(ess) has managed to escape from their one and only encounter with all virginities intact—aside from handholding (which they didn’t have in the first place).
However, this event has ever so slightly opened their mind to corruption; their lust will increase over time, and you must continuously purge them before it’s too late. After all, you’re the only person who can (who they’d allow to) touch them in any sort of manner required to fulfill that duty.
One way to reduce Jordan’s corruption is take it upon yourself, similarly to purging a penitent in the confessional. This is best for keeping lower amounts of lust at bay, but must be done relatively often. To wipe more corruption at a time, you can “deflower” them in the temple prayer room, satiating them while preserving their purity (basically the rite of defilement, except...)
The Bishop is aware of it all, and fully supports this endeavor, as they recognize the toll lust takes on people. Especially someone like Jordan, whom they recommend keeping innocent.
Speaking of innocence, Jordan’s awareness of sex will increase over time as well, mostly by their own efforts. After their encounter with the aforementioned elkspawn, they realized just how weak they had felt as they were, and promised themself to become stronger for the sake of their beloved town. You can either help them acquire a different outlook on the world, or listen to the Bishop and keep that from happening at all.
Actions taken on the job influence Jordan’s perception of you and the temple’s grace—some choices affect them in the same way, while others offer contradicting possibilities. At first, the rest of the temple will ignore you, or even sneer at you, but may slowly warm up to you depending on the decisions you’ll make. No matter how well you may have been regarded as an angelic monk/nun, grace will reset to 0 after coming back to serve Jordan—as a fallen angel, of all things.
As for Jordan themself, they will be grateful for your efforts no matter how they may feel about you, but higher respect might influence the way they act toward or in regard to you. With enough awareness, perhaps they’ll catch onto the less-than-savory aspects of the temple, and even stand up for you should the occasion arise—if they respect you enough to risk disturbing the peace.
At high corruption, perhaps they’ll no longer be able to keep their gaze from wandering over you a little longer than necessary—or their hands from wandering to less-than-appropriate places in less-than-appropriate ways, getting bolder and bolder as their willpower wanes. The more innocent you keep them, the less likely they’d be able to realize what they’re doing on their own, and therefore less likely to stop unless you set firm boundaries every single time.
Allowing their awareness to rise offers many possibilities, regardless of respect—not only to you, but to themself and the rest of the temple—which can be both a blessing and a curse. More awareness may prompt Jordan to actually wander outside the temple, with or without you to help them navigate this dangerous town—depending on where they go, they might start learning more about themself and begin taking care of their own needs, requiring less and less help in that department over time. On the other hand, it’ll risk complicating things in other areas of life, as they grow emboldened to make more and more unexpected decisions regarding the temple—especially if their shifting perspective clashes against the Bishop’s, who will ultimately blame you for any changes in their behavior.
If you’re not careful, Jordan might witness things they can’t unsee or unhear—and they can never be 100% innocent again, no matter how much you try to make them forget.
Should the need arise, they will happily take off some of the burden they’ve placed on your shoulders, especially as their own purity still snuffs out corruption. The simplest way for you to increase yours is by simply basking in their radiant angelic light, but there are other methods as well (mainly through skin-to-skin contact). The more virginities they keep, the more effective any purifying actions are. As long as their corruption is low, of course—otherwise, corruption will be the only thing they can give you.