A player named Borsy brought it to my attention that if for some reason you want to remove all your accessories from being visible on your profile you can only remove accessories that are labeled as “Hat” and I believe the update to different accessory types would be the cause of the trouble.
Here are some pics that they provided that help explain the problem very clearly:
You can see the that “Add to Profile” button is missing and I checked for all other accessory types and the only type that can be removed are those labeled “Hat.”