Hi,
Thanks for your answer. It’s been of great help!
I was indeed in your last case. Everything passed except “Dangerous Props”.
I can now access the homepage of the app. I have yet to try the securipass thing, but it’s currently installed on another phone that I can’t access at the moment being on holidays. As for the second app in which I couldn’t access a payment feature, I can now access it as well.
Here is what I did, in case anybody encounters the same problem. As it turns out, it had nothing to do with the SafetyNet. I was wrong to assume that.
Following piero’s advice, I looked into the build.prop file. After a little search on the Internet, I found out that the two strings causing this error are:
ro.debuggable=1 (should be 0 instead)
ro.secure=0 (should be 1 instead)
(source : detect non rooted device as rooted device · Issue #147 · scottyab/rootbeer · GitHub)
I followed this tutorial to modify the build.prop file.
Since the two lines I mentioned earlier weren’t on my file at all, I added them at the end.
ro.debuggable=0
ro.secure=1
If you’re in the same case as I was in and those lines aren’t in your build.prop, you can still check their values by typing the following:
adb shell
getprop ro.debuggable
# returned 1 in my case
getprop ro.secure
# also returned 1 in my case
# but to be on the safe side, I put it in the file anyway
Once that was done, I pushed the file back on the phone (I had to do an adb remount because I had a read-only error) and rebooted the phone still following the tutorial.
I tested Rootbeer right away and passed everything. I then tried opening the app and the your-device-is-rooted-screen-of-death did not appear. Huzzah! 
As for what the two lines I added to build.prop do, I am not really clear on this. I’ve read on the Internet that it has to do with ADB debugging. I did notice that the ADB root parameter that appeared in my developer settings with the update disappeared. But I can still use ADB as before. And when I try adb root on my computer it still works.
From what I’ve read, it may be necessary to redo all this every time there is an OS update.
I hope this may help other people too even though the title of the topic ends up being misleading, and thanks again piero for your answer. 