What I've tried until now:
Changing window managers with mate tweak -> nothing changed
I downloaded Xubuntu 17.04 and installed it on an usd drive. There it does not work either. So it's not a Mate only issue.
I have on the same laptop a partition with linux mint 18.1 Cinnamon with the same kernel as Ubuntu Mate 17.04. There the switching between tty's works. 
Ubuntu Mate is using a newer intel microcode. So I downgraded to the mint version. -> nothing changed
I thought perhaps it could be lightdm. I changed to xdm. It was not lightdm. -> nothing changed
Than I use grub with kernel option nomodeset. It's the same like i915.modeset=0.
That works, but I got errors from intel ips.
After blacklisting intel ips in modprobe.d it looks a little better.
But this is with the kernel option nomodeset. So I have not the chance to change the display resolution and the external monitor is not recognized.
Linux Mint is based on 16.04. The desktop environment seems not to matter. The kernel and the intel microcode are the same. Something in this case must changed in Ubuntu between 16.04 and 17.04, but nor the kernel or the intel microcode should be the problem.