There is no explicit legislation in Denmark concerning naturism / bathing in the nude. There are only a few limitations on where you may freely practise naturism - eg. it is generally permitted to bathe naked on the beaches.
The public order is regulated in a decree from the Police.
The rules and legislation concerning indecent behaviour and offending public decency also applies to clothes-optional beaches. The only difference is that you may choose not to wear a swimsuit. In all other respects the legislation is the same.
According to the a Police Council (Politimesterforeningen) it is indeed permitted to bathe nude on the Danish beaches. This interpretation is in line with a decision from 1976 made by the Ministery of Justice that bathing and sunning on beaches and without clothes is not by itself indecent behaviour.
Please note the the said decree from the Police also applies to people, who harass naturists. This includes voyeurs or other people, who annoy naturists and thereby disturb the public order.
This is why our general recommandation is: Enjoy your stay on the beach and show consideration!