I'd be embarrassed alright.
And no I wouldn't let them get a sex change and if they got one when they're older I wouldn't approve, but love them all the same. But I'd be fine with them being gay, boy or girl. I'd get a tad upset first, but it wouldn't last.
And knowing me I'll know homosexuality is completely normal and natural but I'd blame myself somewhere along the line wondering what I did wrong and doubting myself as a father and whatnot. Like a little baby... >_>