Everyone tends to say "If s/he were my child, I would..." whenever homosexuality or gender dysphoria is mentioned in connection with musings over how parents must feel/react when their child comes out. Few people admit they would freak out, lest they be labelled prejudiced, discriminatory or homophobic.
I myself have plenty of LGBT friends - yes, I actually know transgendered people as well - both male-to-female, as well as female-to-male. I tend to look at everyone as an individual and form my opinion entirely on them as such, regardless of sexuality, race, age etc.
This does not mean though that I would immediately be accepting, or have a positive reaction, should Creature come out to me one day and say "I'm attracted to my own gender," or "I feel I was born in the wrong body and want to undergo a sex change operation."
I cannot imagine how I would react. Eventually, once the shock would fade away, I suppose I would be ok with it. It would be very hypocritical of me otherwise. But, being ok with it, and accepting it, are two totally different things. Especially when it comes to gender reassignment. How do you wrap your head around the fact that you gave birth to a girl/boy, and will now have to get used to the idea of having the opposite gender as your child? Even talking about them will have to be something to adjust to. Instead of saying 'my daughter' you would now have to say 'my son' and vice versa. It must be rather confusing. Hell, I sometimes get confused as to which gender to use when talking about transgendered friends, since I got to know them in their birth-assigned gender!
I can only hope that if the day comes where I will have to face such a situation, I will be able to do so in a supportive and accepting manner.