I had tamed 5 cats in a snowy village in a newly generated creative default world in 1.14.2. Walking away from the village I noticed they were not teleporting to me. I then decided to test what blocks they aren't able to teleport to...
 
What I expected to happen was...:
When walking a reasonable distance away from the tamed cats, they should have teleported to me, as they were not able to keep up with me.
 
What actually happened was...:
They walked as fast as they could but I walked faster. I kept walking when eventually they un-rendered without teleporting to me.
 
Steps to Reproduce:

1. Stand in an area that has one or more of any of the following blocks:
   1. any type of bottom-half slab
   2. Any carpet
   3. Any bed
   4. grass_path
   5. farmland
   6. snow layer (layers 1-8)
   7. grass
   8. tall grass
   9. fern
   10. large_fern
   11. Flowers (Tall and short variants, eg: rose_bush, lilac, dandelion, alium etc.)
   12. Any stair blocks (may be intended?)
   13. Rail variants
   14. Bottom-half trapdoors
   15. pressure plate variants
   16. ice
   17. button variants
   18. daylight_detector
   19. redstone_wire
   20. torch
   21. tripwire_hook
   22. door variants
   23. Banner variants
   24. flower_pot
   25. lever
2. Make sure there are no other blocks except those listed above around you for at least 20 blocks away to be safe.
3. Have a tamed cat in another area from the one with the listed blocks, but close enough so it is in rendering range.
4. Move away from the cat and to the area with listed blocks
5. Observe how the cat is unable to teleport near the player on any of these blocks.

I suggest trying something similar to the attached screenshot to test this, (A platform roughly 30 blocks above the cats with listed blocks) getting the cats on the ground below the platform, and flying up to the platform and standing/walking around on it near the various blocks.

On the attached picture: A platform made up of the blocks in question; below, the cats, that aren't able to teleport to the player while the player is on any part of the platform; the village in the background.

**Similar to * MC-145021 except more blocks affect cats; wolves; parrots than just snow*