It is one thing to say support equal rights for said minority group in a public opinion poll, and another to vote in favor of an measure/referendum on banning discrimination against a certain minority group. While I am not doubting that a majority are against discrimination in this case. I feel that Social desirability bias may play at a least a small role in these numbers. Over the last few decades we have generally as a society promoted equal rights for minority groups as well as viewed discrimination as wrong. This may lead to a situation where those that are against equal rights may not feel comfortable admitting it to a pollster. While we have come along way in getting rid have discrimination from the workplace/schools/armed forces, we may still have a bigger issue then we might think.
Here is an article on the topic I found
https://www.iser.essex.ac.uk/research/publications/working-papers/iser/2013-04.pdf
