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ParanoidAndroid F-Droid's security is a point but when F-Droid builds the app it is more or less guaranteed, that the app was build from the source code. This is not the case when Obtainium is the installation-source because the signature that can be verified has nothing to do with the Code.
The bigger question here is do you trust them to take care of everything for you or not? If you trust them enough then use them.
ParanoidAndroid If my assumption is correct I don't get why I should trust many developers when using Obtainium instead of only trusting F-Droid. Isn't the Security compromised with each app that is installed and updated via Obtainium?
As I said you are still trusting the developers to an extent especially since as mentioned F-Droid's security checks are rather... Bad and ineffective currently.
In terms of obtainium you are partially correct especially if you do not manually verify them yourself. The concept of the way obtainium is often suggested over F-Droid is that you don't have a extremely insecure source managing all of your apps. Obtainium isn't necessarily insecure or secure in the sources that it connects to (depends on the source of course) but it does have issues that have been discussed which while don't make it a necessarily insecure option they do make it a problematic option as how it handles things in my honest opinion is not a good nor reliable way to obtain apps unless as a last resort which is why I mainly use RSS and just do everything manually including the verification processes.
There's evidently reasons why GrapheneOS doesn't actually recommend or suggest Obtainium.
Because just like F-Droid it is problematic except in some different ways. The only problematic thing they really share is that they both break the Android trust model due to them both being able to basically add any third party source they want while technically being a app store.
Me personally I avoid Obtainium as much as possible except for places where RSS feeds cannot cover. Which so far is only one application so I would say that is going pretty well. And even then I plan to resolve that to where I can get rid of obtainium entirely.
Point being. I trust myself enough to where I can manage everything myself. Because if a developer all of a sudden turns malicious and ships a malicious update. Or the app is spyware. Well I'm rather confident in my ability to be able to notice and detect that and then when I do it's time to pull the app from my Device and feeds. And for the installation process after being notified of an update I use Vanadium to download it (wouldn't trust any browser with lesser security for such a task) and then do check and verify it if possible and then after installation keep a really close eye for any suspicious activity for the initial week of installation. Of course. I do plan to shift from RSS to Accrescent as it matures but until then...
But I know everyone is different and you may not be as confident in doing so. Which is perfectly fine and understandable! After all that's a pretty big position to take for most and some people may just simply not be able to do it for one reason or another.
That's precisely the point I'm trying to make about F-Droid is do you feel like you yourself trust it enough to let it manage your apps despite it's security issues? You can listen to people go back and fourth about pros and cons but not every solution is for everyone. There are legitimate reasons to use F-Droid as are there legitimate reasons to use any app source.
Think for yourself. Do you trust yourself to manage your apps more or F-Droid? Because that's basically what you have to do with Obtainium or RSS is manage security yourself.
Come to your own conclusion on what you yourself want to use. What you think is better for you. Cause honestly this Obtainium versus F-Droid stuff is just going to keep going on and on cause both sides have issues. And it's precisely these reasons why I am not giving you a suggestion myself.
Hope this extra info and explanation helps you make a decision!