How to get Feitian MultiPass FIDO U2F working with OnePlus 3T?
The "Something went wrong" error message was an indirect result of the fact that the device was rooted (+ I have custom bootloader (TWRP), although I'm using stock ROM). I also couldn't use Android Pay in the past because of the rooting although I tried SU Hide techniques for SuperSU. Tonight I reflashed and this time I used the latest beta 14.3 Magisk, which has auto hide feature. 

This Magisk could successfully cloak the custom boot loader and the rooting from SafetyNet, which framework+API is used by Android Pay to see if the device is stock. I assume that the U2F key addition uses the same library as well, because now I could get the BLE part working. NFC is still no bueno. Also, after many tries it become clear that I had to add the MultiPass key first on my desktop using a Chrome browser, and only after that I could complete the rest of the procedure (BLE pairing, ...) on the phone.

The workflow on the phone is weird, because at some point the Bluetooth pairing view got into the background abruptly. I thought something failed again and kept retrying, until I realized that the view is there in the background.

Overall it wasn't an easy ride, but now I removed the phones from my 2FA configuration, and I only have the security keys and the Google authenticator app. You cannot remove that latter one, it's needed for 2FA.

I assume other devices than OnePlus 3T would experience the same thing: if you don't hide the custom bootloader and rooting adequately, software which query SafetyNet will be trippin'.