Adware is marked as an Anti-Feature in the details of an app in F-Droid[1]. Since non-free software is not allowed on F-Droid, and most Ad platforms aren't free software, you're unlikely to find any, though. There's currently only 30 apps with this Anti-Feature[2].
"insecure" is a strong word that shouldn't be used willy-nilly like that. F-Droid recompiles all of its applications to ensure that everything in them is free software, and that the source code provided by the upstream is actually what is in the released binary. To this end, they produce reproducible builds, allowing anyone to rebuild the sources locally and verify that they match.
Which is also how most Linux distros work. So if you use Linux to install software via it's package manager, you already participate in this model. It moves trust to the package repo rather than the app developer.
This is probably inaccurate - for instance I use Librera Reader for PDF and it does use ads - annoying video ads that shows up randomly when I close a document. It is not in the list of the 30 apps. And no anti feature is being declared on the app description. That's only one example that I am aware of.
I use librera reader and I have no ads, are you sure you're using the F-Droid version of the app? If you're not, I suggest installing it through F-Droid, as the play store version may have proprietary code in it. Many apps have different builds for Play Store and F-Droid, with slightly different featuresets.
If you are already using the F-Droid version, it should be reported. The list of anti-features is kept accurate by user reports like yours.
[1]: https://f-droid.org/docs/Anti-Features/#Ads
[2]: https://monitor.f-droid.org/anti-feature/Ads