Here are some solutions that worked for me. I have only tested these on Arch Linux:
Installing lib32-libudev0-shim
This causes Steam’s version of libudev to not load.
Installing lib32-libnm
Steam uses a library called libnm. If a version of this library exists on the system, it uses it; otherwise, the one provided by Steam is used. libnm makes calls to libgudev, which subsequently makes calls to libudev, causing the crash. Using a version of libnm provided by Arch does not cause the crash.
Preloading/installing an older version of the libgudev
Older versions do not call the failing function.
I used Option 2. to solve this issue. Will check in a couple of days/weeks if it works again without this package. But after installing it Steam starts just fine again.