The #1 thing you can do right now is to add a application based firewall to your android phone. It emulates a VPN so all traffic is routed through it, then implements firewall rules based on application, IP address, etc. You can whitelist, blacklist, etc. Most of my apps have zero network access and don't need it. For those that do - I block them from sending to advertising domains. Imperfect but better than nothing.
Android conspicuously doesn't include 'network access' as a permission, for what I can only assume is nefarious reasons. There's no reason my Calculator app needs to phone home anywhere.
The problem though really lies in the network. LTE is GPS trackable inherently. If you want to eliminate that problem, a Pager can work quite well if you are interested in receive only.