Yes, easily: do not put your account credentials there.
Sure, you will be not able to use Google apps, but that's the point, right?
IMO the point is using the ecosystem without sacrificing your privacy -- and you have to go through a lot of hoops on Android to achieve it. Hoops the normal non tech-savvy people won't go through.
Using Android without compromising your privacy and using Google services with the same are two radically different things.
Especially because the Google services run on the Google servers and you have to contact them in order to use them. The same is not true for just using Android. However, the thing regarding Google services is true whether you use them on Android or any other system.
Google Play Services offers a lot of baked functionality many apps have come to rely on.
That's true. However, just like any other third party library, app may use, but they don't have to. It is up to the developer. It is perfectly fine to develop Android apps that do not use Google Play Services.
In fact, if you want your app to run on Chinese devices or Amazon devices, for example, you have to account for missing Google Play Services.
I'll tell that to my mother. I am sure she will agree. Right after she finishes laughing.
No, it's not "very easily". It's not even "easily".