put a rail and and place a shulker near the end of rail ,place a minecart on the rail and push it towards the shulker, when shulker rides on the minecart ,push the minecart ,the shulker seens teleport between the place it used to be and minecart.
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Minecarts won't pick up shulkers anymore

@unknown Seems a bit crazy that they can't ride minecarts. Many of us like to create mob museums. To have one that must be moved with pistons only, especially considering where they spawn, would be incredibly painful. Consider making it so they can't teleport when in a Minecart.
Still in 15w31C, for Shulker riding entities with commands.
Here is video. For command, you might need to stop it at the textbox.
https://www.youtube.com/watch?v=6TY_pjX-arY

This is MC-84456
Ok, there is another ticket for it. Thanks for it.
I think this is because it's an entity which means it should be in a minecart, but the game also treats it as a block, which can't be moved by minecarts. Either way, it's weird.