Require fingerprint to answer call? A friend has a problem with other people answering their phone and thereby intercepting their calls. Is anybody aware of an app, setting, or Android distro that requires a fingerprint swipe to answer an ordinary phonecall?

Google has not been helpful (or my google-fu is insufficient level, below 9000).
Simple Google Fu: &quot;android protect incoming calls&quot; turns up a bunch of apps to protect incoming calls. Most of them use PIN or pattern, though. So: android protect incoming calls finger-print → Hit #1 = AppLock 2:

Android 5.1 supported, Samsung Fingerprint unlock supported
[…]
☆ Lock Incoming Calls

(My Google-Fu must be beyond level 9000 then :))
Hit #3 from that search might be worth reading as well: How to Lock Any App with Fingerprint Security on Your Galaxy S5. Not sure if all this is restricted to Samsung devices, though (and you didn't name yours).