I have come up with the solution to this.

You do not need to uninstall anything or delete or back up database. It is very simple.

Go to extensions then templates manager in your Joomla admin. There you will see the mobile Joomla templates listed along with your current template. they begin with the word mobile. 

Click on each of the templates one at a time. Go to Menu assignment and select none.

once you have done this to all of them, your website will be up and running again.


Enjoy!

MobileJoomla lists such assignments in "Warnings" block at the top right area of "General" tab content (in MJPro it's starting from initial version, and in MJ Standard it was included in 1.2.0).

I guess it is too hiden for so many people to have missed it. Also soon as you upgrade to new version this happens. You do not have the chance to even see what is on the top right as your website will be reading incorrect usage of mobile joomla and you would be panicking by then.

I think the templates assign the menus on update to the latest version.

This needs to be adjusted in the upgrade zip package.

Hope this helps.