Nobody said blanket trust anything. F-Droid is a community project with a framework that allows for disclosing user hostile behavior in apps. By using it and paying attention, we can all make it even better - the exact opposite of Google, whose incentives do not align at all with these goals.
There are plenty of insecure open source apps. To deny that would be to deny tons of security-related CVEs.
Yes, open source software is easier to audit, but does nothing to a) make those audits actually happen (frequently enough), nor b) improves the quality of those audits.
i.e. just because I have access to information does not validate that information. Work still has to be done.
The same can't be said about 'free' (or sometimes even paid) proprietary apps from play store.
What I do instead is monitor Android's traffic with a LittleSnitch-esque firewall and block all apps I don't use. Also, I've disabled auto-updates on non-essential apps. Only Photos, Maps, Chrome, and Firefox are allowed to auto update on my Android.