IDRINKSLUSH I personally don't use the Fdroid app, I use Droidify and install Fdroid repo apps from there.
I guess that is worth noting that it's different if you talk about F-Droid app or the F-Droid official repository.
The app is just a client, and you can change it with something else; Droidify seems to be a good choice.
The official repo is the server(s) you can retrieve the apps from, and if you change the client, you will still be able to use this repository.
There are also other repositories (see NewPipe, The Guardian Project, Molly, etc.).
These are maintained by other people, usually the developers of the published apps, but not always (see IzzyOnDroid).
IDRINKSLUSH Is Fdroid safe?
Long story short:
If you get a Reproducible Build from the repo, it's not different than downloading that from github (sometimes Play Store, depending on developer choices).
If you get an app signed by F-Droid, this has been discussed in the past as breaking Android security model.
When you install an app signed with a key, you can install updates only if they are signed with the same key.
This means that if F-Droid loses their signing keys, you can't update all the apps signed by them.
This also means that F-Droid might arbitrarily add bad code to every app if goes rogue (or keys are compromised).
An old "fight" showed that in the past F-Droid team overlooked or ignored security, leading people to think it's not a good idea to mix this behaviour with sensitive things like keeping signing keys and the like.