Polls like this do not gauge people's opinion. They have to do more with the wording of the question.
If the question were, "do you want males, including transgender males, to be using a woman's restroom", I'm sure they would have gotten a vastly different response.
People, THIS IS OUR FAULT.
We're assuming people are born knowing about and understanding our bathroom issues. We assume people have thought about it. We assume that if they haven't, they're narrow minded bigots who can't be reached.
Well, they don't, they haven't, and they aren't.
People haven't thought about this because WE'VE SAT ON OUR BUTTS AND REFUSED TO EDUCATE THEM. Newsflash: People aren't going to understand our bathroom issues unless we MAKE THEM UNDERSTAND. We need to explain the situation. If people don't understand that it doesn't make sense for us to use the bathroom associated with our birth sex, it's because WE HAVEN'T GIVEN THEM THE FACTS!
Many people have never knowingly met a trans person who passes. Their image of trans women are the caricatures they've seen in the media and the occasional non-passing woman they might have noticed in public. Their image of transguys is probably nil, since they generally pass and aren't portrayed in media at all.
And I guarantee that the cis person is very, very rare who has sat down and asked himself/herself what it must be like to be living as woman everywhere for every purpose but be forced to use the men's restroom (or vice versa).
Alright, I'll get down from my soap box before I fall off and break something.