This common slang term for a useless gift or person is also a slur for conservative GOP Republicans, especially rich, "white," elderly members of the party.
It is a play on the common usage of the term (implying such individuals are useless or even a burden) and upon the wrinkled appearance of the animals.
The phrase originally comes from the actual white elephants of India which were considered sacred property of the king, above doing work, and were given as supposed rewards to loyal subjects, but due to the expensive nature of keeping an elephant and the fact that they were forbidden from making the beast labor the gift could actually end up ruining the recipient, and was sometimes intended to. Politics can be brutal!
I had no idea grandpa was a White Elephant until I heard him talking about wanting to build a wall on the Mexican border!