Tl;Dr: you shouldn’t trust anyone or anything blindly or unconditionally. However, open source software and its community offer compelling reasons to trust it over proprietary software.

Technically, if you do not read all of the source code of an application and all its dependencies, you can never be 100% sure that it isn’t doing nefarious things. For things that require a connection to the internet, you could monitor all connections to and from the application and its dependencies and see if it is making objectionable connections.

However, in my view, open-source software is in general safer than closed-source software. Open-source software can be audited by any who knows the languages the program is coded in, whereas closed-source software can only be audited by the developer or the few parties they might authorize to see it. Closed-source apps can easily hide spyware because the source code is completely unavailable. Spyware could possibly be missed by the community, but it’s still a whole hell of a lot less likely to occur with so many eyes on the program.

And practically, whenever an open-source software gets even close to including nefarious stuff, the community generates a huge hoopla about it.

Also, Google Play Store is not open source! A better example would be F-Droid, which is an app store that is open-source. While I am not aware of F-Droid delivering spyware ala Google, it is still theoretically possible that they could screw up or be corrupted in the distant future. Therefore, we must stay vigilant, even with groups and people we trust. Practically, this just means… check their work once in a while. It wouldn’t kill you to learn a programming language; try Python for quick results. What I do is whenever an open-source software is written in a language I understand, I’ll pick a few files that look the most important and skim them to see that the program “does what it says on the tin”. Otherwise, I’ll check through the issues on GitHub for any weirdness.

I haven’t even mentioned free and open-source software (free as in speech). I genuinely do not know how to convince people who are disinterested in their own freedom to consider FOSS options, or to do very nearly anything at all. For everyone else…FOSS software respects your freedom to compute as you please. We can quibble about different licenses and if and how effective they are at safeguarding user freedom, but at the end of the day, FOSS licenses are at least intended to give users back your freedom. In my view, it is mightily refreshing to finally take some freedom back!