Why does Google keep asking for user names & passwords I don't know?
What does Google have to do with Motorola?
Motorola phones use the Android system which is heavily reliant on Google software and network services. If you want to use these services (email-gmail, maps and so on) you will need a Google login and password to get access. If you don’t care about these services you can disable them individually in settings->Apps&Notification->Gmail(for instance). If you already use some other web mail facility (yahoo for example). You can find a yahoo mail app in the google play store (yes you have to have a google account for the play store also). Or you could just access yahoo mail via the browser that is already on your phone without resorting to a dedicated app. I have not tried this last suggestion and have no idea if the results are even sensible and usable on a small mobile device screen. There are compromises involved in using any “smart” phone/mobile device these days.
If you are adventurous you could install a so-call ROM. Since android is open source you can install a ‘clean’ non-google version of android. You can avoid (or minimally) tracking by google or facebook and others. - longer battery life because of slim down software.
I did install that to g6play - See here
since you are already in ifixit - you are someone who likes to tinker with stuff.