Well, that sounds a little bit too paranoid considering you are using Android (by Google) ;-).
However, you have chosen the right phone for any amount of Google paranoia, see Living without Google 2.0 - A Google free FP2.
If you’re willing to experiment, you could even install other OSes than Android on the Fairphone 2, see oslist.
I tried Sailfish OS alpha 3 myself some months ago, it ran totally fine already, and it is at alpha 4 (see Changelog here) currently, so probably even better.
Ubuntu Touch is starting to seem worth a try now, too.