This actually just happened with the Cannabis referendum in New Zealand. A narrow majority of people voted to keep it illegal. The conclusions from the progressive camp were that

1. It shouldn't have been put to a referendum in the first place. It's a law that only affects a small number of people.
2. A rather influential medical advisory group came out against it and then changed their minds 5 days before the vote
3. The Prime Minister never gave a position on it, but if she said she supported it, YES would have won.

Overall when it comes to this sort of stuff the only reason why people would support awful things is because of lies and propaganda. It is one of our most important duties as Marxists to disseminate the reality to people so that they can get off the consent manufacturing line.