Tamed cats won't sit on the following blocks:

• Trapped Chests
• Ender Chests
• Lit Blast Furnaces
• Lit Smokers

Cats sit on normal chests and lit furnaces, so this is unexpected.

To reproduce

1. Tame a cat
2. Stand by the blocks mentioned above
   → The tamed cat will not sit on them.

Notes:

Cats also do not sit on barrels, but this functionality seem more expected than the other examples, provided the fact that they do not have an opening animation like chests (and thus cannot be locked, and are not "warm" like furnace blocks)