Interestingly enough,
this isn't the first time they've asked the question.
I found this from last summer, where it was smuggled in amongst a survey about other "problematic" illnesses (Dyslexia, ADHD, Anorexia, etc) in the US.
http://cdn.yougov.com/cumulus_uploads/document/o4rdkrwznj/tabs_OPI_illness_20140618.pdf
Back then we had 73% saying we were real and 10% not. Today in the UK, the 10% stayed steady but the yeses were down at 65-66%. Apparently a third of people admit to being racist in the UK, so it could be worse.
I wonder if it was a bit worse today than it might of been because this was a live issue in the news and perhaps on other days it might have been more positive.