I think the phrase ‘intersexed’ is preferred to ‘hermaphrodite’ [which has an ugly ‘side show freak’ implication] these days.
I know a woman who learned when she was 16 [and hadn’t developed breasts] that she was geneticly male: it’s called ‘androgen insensitivity syndrome’, which prevents the male hormones they’ve been making since they were in the womb from having any effect.
She has always thought of herself as a woman, and as a young girl dreamed of marriage and children, but has had real issues with intimacy due to her condition.
She is very lovely, talented, etc., and has taken female hormones to help her outside match her inside.
She actually has fewer ‘male’ characteristics than most women do: all women have some testosterone [and men, estrogen], but in her case it has no effect.
Such people should be treated with dignitiy and sensitivity, but I’m not sure we need to worry much about their position within the Church. If they appear to belong to one gender and emotionally identify with it, thats likely to be all that’s needed for a Church wedding [even though they can’t generally have kids]. They may require hormone treatments and surgery to completely fulfill that role, but it is a very different thing from the transgendered person.
If they see themselves as intersexed and wish to fulfill a different or dual societal role [some do], then odds are their sexual practices are outside the bounds of Christian marriage anyway.