You do not need to worry about the privacy because Google will never be able to access your private posts and data. Only public posts will be available on Google search. If you just want to search for Facebook posts, you can still use Facebook search for searching. But this will be helpful if you are searching something on web and there is a Facebook post offering the content you are looking for.
This is a win-win for both companies. Users will use Google search via mobile app to take advantage of this feature and users will end-up spending more time on Facebook app.
As of now, we have no confirmation when this will be available to all users. We are trying to get more information about this and will update this post once we have clear information.
Source: WSJ

