That’s a lock-in Google puts on purpose on Android. Don’t worry, Apple services have lock-ins too, 
If you only need read-only access to calendars, I suggest ICSdroid. When someone shares a Google calendar to me (although I try to convince them for not doing it that way), that’s the option I use.
Otherwise, you can try following this 2013 Mozilla post with DAVdroid.
Third option is trying microG and installing Google Calendar from Google Play (or searching the APK online). I can provide further help for this.
Fourth and last option is installing a GApps minimal package (like OpenGApps pico) and so letting Google control your phone.