There are two parts to this. The basic standards based auth stuff "sort of" works. Everything else requires a browser plugin. One of the Debian dudes (of grep.be fame) maintains a Linux version that works in many cases, but for some reason many non-government organisations require the use of a different plugin, one that only works on Windows and mac.

As an aside: signing things has a particularly awful UX. I never know what I'm signing, I have no way to verify that what's on the screen is what's being signed. And then there are orgs that use eID based PDF signing, which again requires different plugins. In short: a shitshow.