Yes, but the idea is that because the code is open source anyone can look at it and determine on their own whether it is in fact safe or not. Generally speaking the open source community is very good at figuring this kind of stuff out but I would say your fear is not necessarily out of place since nothing is 100% guaranteed. That said though, the more popular FOSS apps are quite safe.

By default, FOSS is no more secure or privacy protected than proprietary software. However, it allows the community to peer review the code. So, a popular and active FOSS project can be trusted to be honest and not do nefarious things to your data or devices.

Check activity on their code repository - Stars / Followers and Forks says something about popularity, Issues and pull requests tells you about activity (check comments or check recently closed issues and pull requests), as does the code commits itself.

Edit: Changed wording from secure to trust / honesty. Not all code focus on security; in fact, most code doesn’t.

You mention the Google Play issue. That is an example of a disadvantage of closed source (Android is open, the Google Play Protect is not). Google Play Protect is essentially static code analysis. Think of it almost like antivirus. It tries to look for anomalies in the code itself. But it's not great. It can be tricked. And we don't even know how good it is or what kind of checks it does.

FOSS code has many people looking at it. You can compile it yourself. It's extremely unlikely for something that's remotely popular to have explicitly malicious code in it. Is it impossible? No. But just as you get folks deep diving video game code assets, you get people looking at code of many FOSS projects. Likely because they either want to contribute or make changes.

It comes down to it being easier to find malicious actors in FOSS. Its just more difficult to hide than closed source.

Why would you think closed source is any safer for any of the same reasons but worse? Closed source can just as easily (arguably more easily) steal your info (and many did but bury it in EULAs).

How do you know if a closed source application is stealing your data?

With open source, you can learn to read it, or talk to a community of people who know how to read it. If even just 1 in 500 people who downloads the software looks at the source, there are external eyes on it. Whereas with closed source, no one but the creator is looking.

Biggest thing is to still only install software you trust.

One more note about safety when it comes to open source or FOSS, is that you should use only the main repository and distributions provided by the official team. Often people clone existing repo, insert malicious code and publish it as their app on play store etc.

No, open source code is no safer than closed source code by default. What it does is gives the opportunity for people to verify that it’s safe, but it doesn’t mean it is safe. Also just because some people have “verified” that it is safe doesn’t mean they didn’t just miss the vulnerabilities or nasty code.

In terms of telemetry, free software has the advantage over the proprietary counterpart.

It's a lot more complicated to hide telemetry without the user knowing in free software.

You could always use a network tool, like iftop, to see network traffic on your PC. That could be a way too see if a program is phoning home. But you'll probably want to use a suite of tools.

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!

No. But more safe than closed source.

Tl;dr: Don't download random APKs from the internet, just because they claim to be FOSS. Just get them from F-Droid and you're safe.

Long answer: Depends on the project. Look how many people use it. If it's a bunch, chances are other people also keep an eye on it. Even better if you get that sofware packaged. That means from the package manager of your linux distribution or - in your case, using Android - from F-Droid. This way somebody from that team has a look at it, and F-Droid even strips all those trackers from Apps. I'd say chances for a virus/spyware getting through the F-Droid process are close to none. Not more than chances are of a virus slipping past Google's antivirus.

(Play Store doesn't do anything against excessive tracking.)

You shouldn't see trustworthyness or trust as a binary system of full or nothing.

You should assess - to your and the products possibilities - and then weigh risk and necessity and value.

Source exposure makes it more likely people may look at it, without cause or when something seems surprising or questionable. Source available alone doesn't mean you'd see concerns though - you'd need an obvious platform or publicity.

FOSS may be funded and implemented by voluntary work or paid or sponsored, with or without control by the involved parties.

Security scanning is a best effort weighing known and similarity and suspect parts against false positives and user and publisher inconvenience and hindrance. It can't be perfect.

Android Play Store security scanning can only scan for some things I'd consider security relevant and likely largely ignores questionable behavior that does not endanger device security.

Established projects are more trustworthy than those that are not. Personal projects with a clear goal are more trustworthy because of likely hood of good intention and personal interest than those who seem obscure or unclear.

Don't trust blindly.

Safety is a big topic and theme. So such a broad question can only be answered with broad assessment and overview.

Is FOSS really safe?

It's not an attempt at edginess, but the answer is that in the long run, IT NOTHING is safe. It might be now, it might be for some time, but theres no guarantee that even the most dependable piece of software will get some new update that will break some of its functionality, or the OS will interfere with it, thus breaking it.

FOSS? It's safe as a principle. If anyone has the access to the code, then any suspicious inclusion to it will be spotted quickly and patched up.

...but the reality isn't as straightforward.

A question i always ask myself is, if we can see code on github for example, it still doesn’t mean their release has the same code right? They could actually compile their program with some extra stuff that sends data and just add that version on github release page, but the code itself would be clean on github right?

You wouldn't know unless it's checked by you or someone you trust, but IMO open source should generally be better cause if you're doing shady stuff you're probably less likely to make it public. Also projects with lots of activity by different people are usually safer.

Here's an article