No they don't. They haven't been deprived of anything. There has to be a candidate disqualified from running because of the law, and that candidate can sue, but voters don't have a case until a client is disqualified from running for office by his/her failure to comply with the law.
Only a crook or a liar would refuse. The request is not unreasonable. What is unreasonable is Trump's refusal to comply with this request.
Privacy is important. Recall, that is what RvW was founded upon.
The issue isn't whether privacy is important or not, it's whether the voters have standing to file the lawsuit. I would say "No they don't", not based on the Constitution, but because no voter has been harmed by this law, because no candidate has been removed from the ballot because of this law.
Unless or until this happens, the voters have no standing, and no case, because the voters have not been harmed. The first thing you have to prove in a lawsuit is that YOU, the Plaintiff, have personally suffered harm because of this law. Since no candidate has been removed from the ballot, no voter has been harmed.