Really, the only thing you could do is end participation in the walled app gardens, force a VPN connection to a trusted service provider and only use audited open-source client software. Which is closer to the tiny blip on the market that is the Mozilla Smartphone than anything else that actually exists. Or I guess you could root your device and use the local hosts file to prevent all communication with whatever service providers you don't want to talk to. I have no idea how that would impact things like PRL updates or other basic mobile device functions, and there's really nothing you can do about the SIM or SIM-like transceivers you might have.
And I suspect you'd probably want to route everything possible through TOR starting at a non-logging VPN service to add some deniability.
Since the OpenBSD people aren't talking in any serious way about solving mobile device paranoia on that level, we're probably SOL.