The Red Light district is pretty safe as long as you're not stupid and venture into unlit areas or away from the obvious walkways. Stay with the other tourists, don't wear jewellery, don't use shoulder bags, don't put wallets in your back pockets and don't do anything that will make you stand out in a crowd. All things you would tell someone if it was their first trip to London, Paris etc. Careful of pickpockets around the train station, Dam Square especially but basically anywhere. And be careful with taking pictures. If you insist on taking photos in the Red Light District then do it discretely and don't take photo's of the working girls directly, they don't appreciate it.