There are plenty of pieces of open source software running on operating systems that were contributed by people who are effectively anonymous.
Also, it doesn't seem like a contributor's overall character would be a great measure of how malicious their contriubtions are, as evidenced by plenty of examples of assumed good people eventually doing bad things.
At the moment, I do rely on reputation before I trust open source software. But in the case of an app store, I can trust the reputation of the store. I can trust that the app store has to work to uphold their reputation which is their motivation for maintaining a good track record of identifying problem apps. I agree this is far from perfect, but I think it’s much safer than relying on open source.
I love the idea of open source and I hope that it will never be replaced by app stores, but I don’t feel that software is inherently more trustworthy if it’s open source.
Verified trustworthy is too high a standard to hold to software. Take for example Log4j, an open source logging library used by many enterprise Java apps worldwide, had a huge vulnerability existing in its code base for over 7 years. Even with its widespread use and open sourced code, the exploit was not reported in a timely fashion.
Thus I’m left with reputation as the only practical means of determining trust; imperfect as it may be.