brook You can install these apps using Obtanium from github, and any of these apps can become spyware, malware, adware at any moment. No guarantee what so ever. E.g. repos can be hacked, authors can sell the project or turn malicious.
And Fdroid can also be taken over at any moment. At which point every single app that is available on their repo is now at risk due to them using the same signing keys for all apps. I would rather trust individual apps with separate signing keys so that any harm done is isolated to specific apps, which can be disabled or uninstalled individually.
You have to rely on reputation of 10+ different people, some of which are unknown and have accounts with only 1-2 years history. Any one of them can screw you totally at any moment, push spyware and only lose their 2-years anonymous developer reputation (almost zero loss).
Then don't use such "new/unknown apps". Stick to more well known ones. Github has a star system. Use apps with lots of stars (and therefore more attention on them). This is true regardless of whether you have apps on Github with 10 stars, or apps on Play Store with only 2000 downloads.
Obtanium does not even provide any verification that apks are in any way connected to the source code from the repo, it takes them from Release page, that can contain anything completely unrelated to the source code in git repo itself.
This is more the fault of app developers themselve if anything. Developers can and should be providing hashes that people can use to verify installations. The lack of this being the case shouldn't really be pinned on Obtainium.
You install all apps that have their code some-what checked before making apk, there is at least some verification, probably better than in google store, due to projects being FLOSS.
GOS developers have repeatedly stated that the "checks" are basic/flawed and don't really do much, which would therefore lead to a false sense of security. The example typically used is Wireguard adding their own self-updater (against Fdroid's rules) and Fdroid didn't even notice till much later.
You almost only have to trust F-Droid, the project that is well-respected and exists for 15+ years. Reputation to lose is huge. Main team members are also not anonymous.
"Well-respected" by who? From what I've seen, they have repeatedly shown to not care all that much about security, often putting software ideology above security. I've not really heard good things about them from the GOS devs either, who I frankly trust and respect a lot more than the Fdroid team.
So, how can one consider Obtanium or grabbing apks from github repos to be a secure way of managing your software?
Its not so much that Obtainium is a "secure" way to get apps. More that it is better (in the minds of some people) to skip unnecessary middle men and get apps directly from developers themselves, especially when the signing keys of individual developers are used instead of a universal third-party (Fdroid) key.