The following pets are NEVER for trade:
(Get ready, it's a long list)
Aaja
Crimson_Ghost
DollSteak
Horror_Business
Kosima
OneThirtyEight
Shysti
SkullsAndStars
Utero
Zerainia

Probably NFT (Due to NO good offers):
Pyroglyphics
Rexella(EDIT*currently lending)
SunShowers