A pollster has your identifying information when the poll is taken. One assumes that identifying information is stripped away before the results are tabulated, but there is no legal requirement for that to happen. Because the information exists, there is nothing preventing the misuse of that information.
Well, considering I had to fill out numerous forms for every weapon I purchased, and I have a concealed carry permit on top of that, I guess they wouldn’t be finding out anything they didn’t already know.