Yep. It's really stupid that natural weapons don't count as finesse - especially for a highly dextrous race like Tabaxi - but, officially, they don't (the couple of GMs I've pulled have all said they would be finesse in their home games).
Here's the strange thing: many monsters in the Monster Manual that use natural weapons must be considered as finesse because their to hit and damage doesn't compute if their natural weapons were not. Since we're talking about Tabaxi, let's take the cat as an example. Its claws to hit is +0. The only way that could happen is if the claws were finesse. If they were not, then the to hit would be -2 (Str Mod -4 plus proficiency +2).
OTOH, Jeremy Crawford explicitly said that they are not finesse. So, for AL purposes, tabaxi & lizardfolk natural weapons are not finesse. Otherwise, homebrew applies.