Polar Bears will not get in boats, have tried on singleplayer and multiplayer. This issue does not seem to affect any other mob except polar bears.
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@violine1101 Polar bears can get in boats in version 1.13.2 I have attached pictures of this.
Panda's get in boats without any issue. I assume polars and pandas share the same model. So why would one be able to and the other can't?
really annoying especially when I try to transport polar bears to my house or in different locations throughout a world
I've tested this and it seems that the polar bear can't get inside a boat (except for the use of commands using the Passengers tag.) instead they push the boat.

No large mobs can enter boats, since their bounding box would be larger than that of the boat.
As far as I understand it, all mobs that have a hitbox that is larger than the hitbox of a boat cannot enter a boat. Other examples for mobs that cannot enter boats include horses, donkeys, and mules.