Is there a ubuntu supported X.org alternative (i.e. with security in mind)?

Wayland is supposed to be a complete replacement for X, not an addon, and it addresses the problems which concern you. Note that at the moment Wayland is not production ready and there is limited driver and toolkit support for it.

It seems that Ubuntu does not have any plans to integrate Wayland at the moment, and wants to create its own display server called Mir, which may also address some of your security concerns. Mir is also not ready for general use.

DirectFB is a bare bones solution for embedded systems which gives programs direct access to the video card's framebuffer. It does not have any security mechanisms.

Another solution is not to run a GUI at all.