To me it looks like this bug is now solved.
I remember having the same problem months ago, but today it seems to work fine
(on a foreign distro).
Guix:
---
guix 6eded1a
repository URL: https://git.savannah.gnu.org/git/guix.git
branch: master
commit: 6eded1a04186e3118b293486b038c994e05efedf
---
Icecat:
---
icecat 78.14.0-guix0-preview1 out
/gnu/store/xwzp1lj8b429yc9nbx3nwy1ia9r1sr2x-icecat-78.14.0-guix0-preview1
---
It worked both with https://u2f.bin.coffee/ and other services.
Note that I'm "cheating" a little bit though: I'm using an emulated device, not
an actual USB device (but the same emulated device previously didn't work with a
Guix-built icecat).