Firebase App Indexing has two components:
- Public content indexing. This makes it easy to associate in-app versions of your public web content.
- Personal content indexing. This is an Android-only feature that allows you to keep a local index of your app's content so it turns up during on device search.
In the first case you are only indexing public content, so you should not share any private information. Compliance should therefore be a non-issue.
In the second, the index is stored on-device as part of Google Play services, and only summary usage statistics are sent over the network. How that effects regulatory compliance depends on your usage and the type of data you are storing, but hopefully it helps you make a decision!