Good question, seeing how Android and google are partners.. couple of things you can do is limit what google products are on your phone at one time or all the time.. simply deactivate them or use an app made to quarantine google products so that they do not reactivate. (Opera Max)
Secondly, and the hardest way to remove or forcible quit using Google products it to switch to another smart from brand or create your own brand of smart phone products.. But I like the first option better.
For instance, Opera & other Opera products/software/apps can help one control what Google/Android apps are active on your smart phone.. To me using opera max and other opera products has helped reduce most all of the Google products I don't want running on my smart phone at any point in time.
But as always there is a double edge sword.. if you locate an app you want, 9 out of 10 times, you'll need Google play to access and install your app discovery. But before you install anything, I'd check Opera's app store (though limited on what is offered) first.
Guess what I'm saying is that you can't get rid of everything Google related on your smarty, just reduce what is seen, heard and runs in the back ground.
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