The interested volunteer didn't give any information about the role of the woman he is interested in, except to say she is generally like a supervisor. So this is reading into the situation, but it also seems likely she works at the church. If she is the Pastor, or Christian Education Director, she may be bound by Clergy or church worker ethics not to get romantically involved with a parishioner. Those limitations can seem overly strong if the two people are otherwise eligible and suitable, but it can be like an office romance, but worse, if things go badly.

Why does the volunteer have to be a male?

Yes, people who are homosexual attend and volunteer in churches. However, most would not seek their romantic partners there, because in most churches, homosexuality is viewed as a sin, at least by most members. Even in accepting churches, it is often viewed as something to overcome. Therefore, it is extremely unlikely that a lesbian would be considering asking out someone who is the leader in most of the church activities at which she participates.

It would be awkward enough for a man to continue to work with this woman having asked her out and being rebuffed. It would be much more so for a lesbian to ask her out only to discover she is vehemently anti-gay.

Hey, I'm the volunteer, and I'm a guy ; ) But to be discussed as a lesbian for a moment was quite interesting. To clarify, she's not the pastor, (she's his daughter) and isn't employed by the church (though I would definitely say we "work" for the church.)

As I stated elsewhere, I'd take it slowly. Ask her to something not too date-like, like for coffee after an event. If that goes well, ask her to something like dinner or whatever the standard date fare is where you are. Or, during coffee, you can just tell her you'd like to go out with her, if she's okay with that. Just make sure she understands if she says "no", it won't affect your working relationship at church.