I think it's something that shouldn't be judged by the opinions of other people but by your own heart.
Personally, I'm bi, so I will grant you that I'm already not in the majority because I don't find either standard arrangement yucky (quite the opposite, in fact), and I'm female so it's more socially acceptable for me to be in a non hetero-normative relationship. So I can't say I have as much riding on my answers as most of the people (guys mainly) here, but I would definitely date a transgendered person.
Heck, if we consider the term "gender" as meaning compliance with the classic long hair and dresses versus frat boy, and "transgender" as noncompliance with those standards (which is in fact what the term gender means... societal roles of people biologically sexed one way or the other), then there is a certain set of "transgender" lesbian women who dress and act like gentlemen that I find extremely attractive.
I think it's interesting how many people are willing to be friends with a transgendered person but not date them. Yes, the "acceptable company" bar is much lower for friends than it is life partner no matter what issue we're talking about, but I find the contrast between the "HELL NO" and "It might be awkward at first but I think I would get over it" average response to the two questions is an intriguing dichotomy. If the answer to the second is true, why can't it be the same for the first?