I am uncomfortable with the idea that if this isn't something you would want, you are somehow in the wrong, bigoted or narrow minded. I think that for a lot of people dating = sex, at some point, eventually, after a few dates people normally begin to get intimate - don't they? You don't date someone and not end up kissing them, and then end up, eventually, if you like each other, in bed with them. And THAT'S where it changes. This is a person who, at the moment, has female genitals. If you are not a person who is sexually excited by female genitals - this is going to be a problem for you at that point! Surely? That doesn't in itself make you any sort of bigot!
If there's not going to be sex, and it's just going to the cinema, going for a meal, watching tv together etc etc then it's just a person who looks, sounds, acts, feels - male and if that's what you like then you're going to be fine aren't you? and it wouldn't be an issue but I don't think that it's unreasonable of someone to say that they really don't want to get into bed with someone who has a vagina and clitoris and dive in face first if that's not their sexual preference!
That isn't in itself bigoted. It is about sexual organs and which set does it for you! If that isn't accepted as reasonable, and is considered bigoted then by extension everyone who is heterosexual would be a bigot for not having sex with a person of the same gender and everyone who is homosexual would be a bigot for not having sex with a person of the opposite gender! You have to accept and respect sexuality in all its forms and that includes the right to not want to engage in sexual behaviour with someone who is in possession of a set that is not sexually attractive to you!
I think it is unfair to say that this is a person who considers themselves male, has had some surgery, but has not had genital surgery and therefore still has female genitalia but you must disregard this and be sexually attracted/active with them or you're a bigot.
I think it would have been better to split the question into two.
1 would you go on a date with a transgendered man who had not had the genital surgery and therefore still had female genitals
2 would you have sex with a transgendered man who had not had the genital surgery and therefore still had female genitals