I worked at Google before, so I trust Google more than these random organizations that claim they are better than Google at handling sensitive info.
Answer: you cannot.
Any time you log into a Google account just to use the Play Store, Android will instantly starts syncing all your contacts and you can't prevent that. You can't even toggle airplane mode as a network connection is required to login. And you cannot configure Android not to sync all contacts data with new Google accounts by default.
I bet Google has syphoned the details of every single person on Earth (without their consent) and I have to trust them not to use that?
F** em
I don't think these projects claim they've got better infrastructure for handling private data, just that they won't sell it to advertisers. I trust Google are experts at handling my data, I just don't want them to.