While playing around in a Singleplayer Creative Superflat world, I noticed a bug with rideable animals. If a Command Block is set up to "Repeat" and "Always Active" with the command to teleport a tamed and saddled rideable mob (Pig, Horse, etc. [Tested list at bottom]) to a set of coordinates, and then the said mob is ridden by a player, the mob is not affected by the teleport command. Once the said player has dismounted the said tamed rideable mob, four unexpected things occur: 1. The said rideable mob is still not affected by the teleportation command; 2. The said rideable mob is in a peculiar state where it has "half of its pathfinding AI," in which it is able to look around and turn, but not able to move nor make a sound (I also found something else technically falling under this category in which if a camel is in this state, it doesn't take any knockback); 3. The player teleports to the specified coordinates programmed into the Command Block which was programmed to teleport the said tamed and saddled rideable mob continuously (tp @e[type=minecraft:<rideable mob>,limit=1] <x> <y> <z>); and 4. If you wait a bit, it will act under the influence of the said Command Block programmed to be teleporting the said rideable mob to a specified set of coordinates. In addition, after that, if the said Command Block programmed to be teleporting the said rideable mob to a specified set of coordinates is broken/deactivated, the said rideable mob will teleport once to the specified set of coordinates and then act as it normally would. Plus, if the said rideable mob is already being ridden, the teleport command has no effect on it; once it is dismounted, it will continue to defy the teleport command until, as mentioned two sentences ago, it eventually obeys the command (until the Command Block is broken/deactivated, as mentioned in the previous sentence.

*Only works with saddled mobs.

Works with horses, mules, pigs, donkeys, camels, striders.