There are other, sensible reasons for such a law. Many strippers engage in prostitution, and many have a history of drug problems. Education and safety training, and simple disease control, can be profoundly eased by reaching out to the registered strippers. It's also a way to check the age of employees, and try to keep children, especially runaways, out of that dangerous line of work.
Such a registry is certainly subject to abuse. Sex workers are certainly subject to stalking, and many families or former sexual partners who would harass or even endanger them. Others are just trying to make ends meet to take care of family and don't want their families to discover how they're paying the bills.