He may have to move them around a bit (because they're only available on the fleet ships now), but they don't have to be removed. The headings can say that the alternate C-Store costume now requires the fleet version to get it (unless you've bought it before Season 6).
You realize this means the price of the ship costumes have increased by about +300%, right?
Instead of just buying the costume for the original low price, you now need 4(!) Fleet Ship Modules to get the Fleet variant ship with accompanying costume.
And I don't think it will be account-wide either. There is no indication that it would be, so I am forced to conclude that it is a per-character unlock.