Alternatives to Google Contacts
Sebastiano LicciardelloWorks on MicroG?
You can use it only as manager. You can't sign in with your account..
Open Source Manager
AOSP / LineageOS Contacts
Simple and reliable. Already included in many custom roms
Aurora Contacts (not released yet)
It will have graphics updated to the new material design and numerous functions and customizations.
Simple Contacts
A simple app for creating or managing your contacts from any source. The contacts can be stored on your device only, but also synchronized via Google, or other accounts. You can display your favorite contacts on a separate list.
Open Source Sync
VCard + Any Cloud or Storage
From AOSP/LineageOS Contacts you can export your contacts as vcf file. For simplicity you can save this fale in a backup hard disk, cloud telegram, or any cloud services. You can do this once a week or whenever you add contacts.
DAVx⁵
DAVx⁵ is a CalDAV/CardDAV management and synchronization app for Android which natively integrates with Android calendar/contact apps.
How to sync with Google Contacts and Calendar
EteSync
Secure, end-to-end encrypted, and privacy respecting sync for Android, the desktop and the web. Currently supports calendars, contacts and tasks (using OpenTasks), with more on the way. In order to use this application you need to have an account with EteSync (paid hosting), or run your own instance (free and open source). Check out https://www.etesync.com/ for more information.
Closed Source
Not yet