I used to be able to change my costume. My hats, item, pants, clothing, etc for my alien. But it seems I can only change my skin color between blue, red, or green. Even this hat is stuck on and I can't unequip it.
I have also been having issues equipping and unequipping things. Some items work, most don't. I can seemingly unequip most items just fine but I'm at a loss as to why. There also appears to be a few duplicated items, such as the valentine's day shirt
A lot of stuff show up but you don't actually own it. You try to equip it but you cannot save because you don't actually have it in your inventory. You have to spend the arp in the marketplace if you want to use that specific item.
Anything you have redeemed in the marketplace should be wearable! There was a bug a while ago that added items to your profile that do not save, so those items won't work, but the customization should be working correctly.