I can imagine a case where people would put themselves at risk of physical harm or harassment by signing a petition if their name were later publicly disclosed. For example, petitioning the government not to go to war at a time when the country was clamoring for blood. I think we can relate to that example. So, I don’t dismiss the concerns of anti-gay rights petitioners when they ask that their names not be disclosed. On the other hand, when your petition is actually part of a legal process for putting a referendum question on the ballot, there has to be disclosure because there are eligibility standards involved. The public deserves to know whether a sufficient number of legal signatures have been obtained to put the question on the ballot.
Strictly speaking, it shouldn’t matter whether the issue is controversial or not. If you are petitioning to reinstate Jim Crow laws or petitioning to keep Christmas a federal holiday, the same law should apply to disclosure. I do think it is interesting, however, that anti-gay rights organizers feel that their position is odious enough to inspire a violent response. It’s not a legal principle, but as a political matter it does make it harder to abuse the referendum system to disclose the identities of people who are pushing for a referendum. If you don’t want your name associated with what you believe, chances are that your beliefs shouldn’t become law. That’s not always true, but, for the most part, it is.