Can I play the new Minecraft for 3DS on the new Mario Kart 7 2DS?

It will work on any of the 'New 3DS' family, which does include the New 2DS.
The New 2DS is just a New 3DS without the 3D screen function.

All 3DS games are compatible with the 2DS. The only difference in hardware, as Cantra pointed out, is the lack of a 3D function.

No. Its only for New 3ds.

You should be able to

Yes. The 2DS and the New 2DS XL just aren't capable of using the 3D features that 3DS family has. It should work perfectly. I don't think the 3D function is used much anymore.

Minecraft for 3DS.