My version of DNN is actually 6.1

When I delete profile properties in the DNN Manage Profile Properties section, the profile property is still listed when a user edits their profile in Active Social.

This is because the profile properties are still in the database, but marked as deleted. There are posts here on the forums explaining why AS does not support the Deleted property, but it has to do with the module supporting various versions of DNN.

You can delete the properties completely from the database and they will not be displayed.