I published my site a few days ago and it looked all fine on desktop and mobile. Then I connected it to Analytics last night without changing anything else, and now my mobile site is completely messed up.
Analytical service would never do anything to your page layouts.
It is just that your layouts are not properly built to be responsive. You are using fixed width in many places which is not the best way to do it. If you really want to set certain width then keep width: 100% and apply max-width: 1000px
Just to be sure, you can remove the analytics code and check how your page is looking.