I've been messing around with
Coin of Many Faces and it seems that cats don't want to sit on the lap when a character is transformed by this item. The original characters are fine.
I haven't tested transformation from other sources, maybe it's worth a more deeper investigation.
Of course we don't talk about druids, shamans or worgen, okay?
(On the other hand, it would actually make sense that a cat doesn't trust an unfamiliar shape.

Like they ever trusted the familiar ones anyway.)
I have compiled community knowledge & data about pet battle abilities!
https://www.warcraftpets.com/community/forum/viewtopic.php?f=3&t=19507