Why would Frieren need a chastity belt? She's not one of BaalBuddy's elves.
Chasity belts aren't only for the girl to not persue relations, it also helps protect them from potential suitors or rapist as well. As well as Men taking advantage of them if they get drunk or drugged. IF Frieren wants to remail loyal to Stark and if she knows she's a popular girl, she could willingly wear one to give Stark an ease of mind.