As the title says, tamed pets (so far only tested on dogs and cats) don't teleport when they are actively trying to navigate an obstacle.

Behavior I've noticed is when they are behind a closed door they won't teleport but will get real close to and get stuck. Dogs seems to do fine with the door open but cats sometimes will refuse to go through even if it is open. Both of the animals won't teleport at all while swimming, causing them to unload with chunks and be "lost" until you happen to load that chunk again.

Here is a video showing the odd behavior.

https://youtu.be/3u_gVzudXkc