TL;DR: Update immediately, especially if SSH is enabled. xz versions 5.6.0 & 5.6.1 are impacted. The article contains links to each distro's specific instructions of what to do.
Current research indicates that the backdoor is active in the SSH Daemon, allowing malicious actors to access systems where SSH is exposed to the internet.
In summary, the conditions for exploitation seem to be:
xz version 5.6.0 or 5.6.1
SSH with a patch that causes xz to be loaded
SSH daemon enabled
Impact on distros
Arch Linux: Backdoor was present, but shouldn't be able to activate. Updating is still strongly recommended.
Debian: Testing, Unstable, and Experimental are affected (update to xz-utils version 5.6.1+really5.4.5-1). Stable is not affected.
Fedora: 41 is affected and should not be used. Fedora 40 may be affected (check the version of xz). Fedora 39 is not affected.
As far as I can tell running xz directly should be fine, but for the extra paranoid check the version of the xz-utils package. If it is safe, it will be either less than 5.6.0, or it should be 5.6.1+really5.4.5-1 (xz 5.4.5 with a spoof version number to ensure compromised systems get the update).