Players and mobs added to teams with "nametagVisibility" set to "never", as you might expect, do not show their nametags. However, non-living entities (minecarts, boats, interaction entities, etc.), per changes in 1.20.3, seem to ignore this setting entirely, despite by all other accounts being added to the team in question. (This does not, incidentally, apply to other team settings such as collisionRule; nametagVisibility seems to be the exception)

Aside from just being inconsistent behavior, this creates issues for mapmakers or datapack developers that may have assigned names to their interaction entities for easier debugging, or that previously used renamed minecarts for GUIs, who now find themselves surrounded by floating text. This also leaves those affected by MC-266885 without a workaround.

Likely related to MC-166450, though armor stands at least don't show their nametag at all unless a flag is specifically set.

Steps to reproduce:

1. /team add noname
2. /team modify noname nametagVisibility never
3. Summon a minecart

   /summon minecart ~ ~ ~ {CustomName:'{"text":"Big Dumb Floating Label"}'}
   

4. Add the minecart to the team

   /team join noname @e[type=minecart,distance=..5]
   

5. Look at cart, notice that the name label is visible
6. Verify that the minecart is on the team and that other modifiers work

   /team list noname
   /team modify noname color red