Should I disable Google contacts in my iPhone Settings?

Yes.  The Contacts Sync app works best when it syncs your Google contacts with either iCloud or iPhone.  With your iCloud or iPhone contacts containing the same contacts as your Google account, there is no need for your Google contacts to be enabled in your iPhone Settings.  Having it enabled may even lead to duplicates.

To disable it, go to your iPhone settings > Contacts > Accounts, find your Google account, and turn off "Contacts." It will warn you that your Google contacts will be removed from your iPhone, and that's safe to do as they will remain at contacts.google.com and will be synced using this app.

Video showing how to disable a Google contacts account (iOS 11):

Please note that syncing a different Google account with this app than the one(s) configured in your iPhone Settings will not create a conflict.

This help article relates to the iPhone app called "Contacts Sync" which can be downloaded here:
https://apps.apple.com/us/app/contacts-sync-for-google-gmail/id454390333
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