So now that you've got Firebase Cloud Messaging (FCM) installed and you've just run the project but you run into the following message: FirebaseInstanceId: background sync failed: INVALID_PARAMETERS
After finding this page, https://github.com/firebase/quickstart-android/issues/54, it turns out that you just need to uninstall the app for all users on the device and then install it again, I guess the registration for the service only happens on install, I'm not too sure, but what I do know is that this solution works.
Something else that could solve your issue is to re-download the google-services.json and the message should then disappear...
One thing to remember when working with the google-services.json is to make sure that you specify its Build Action as GoogleServicesJson within the files properties, further details on how to do this can be found on the Xamarin website.
After the two above steps, you should now see the following message when you run the app: "FirebaseInstanceId: topic sync succeeded".