Update: So it seems that the report below was incorrect. I initially wrote that Valve was banning Linux users with Linux usernames that included the word 'catbot', but Valve has said those claims were a "tactic employed by cheaters to try and sow discord and distrust among anticheat systems".
It's a bit confusing because a Valve moderator on GitHub, as you'll see below, initially seemed to confirm the story by saying that the banning of users was "deliberate". But another Valve employee has since clarified the matter in a Reddit post.
"VAC will not ban you for simply having catbot in your user name (either your Steam profile or on one or more of your Linux accounts). The bug report—and I suspect many of the posts in this thread—are a tactic employed by cheaters to try and sow discord and distrust among anticheat systems.
"VAC has many different types of detections and we cannot discuss what they do publicly because doing so makes them less effective. However, one thing I can disclose is that all detections require that the detection occur while a user is actively cheating and connected to a VAC-secured server.
"Linux historically hasn't been a problem for cheating--the base rate of cheating is significantly lower on Linux than it is on Windows. Unfortunately, a 'healthy' community of cheaters grew up around catbot on linux and their impact on TF became large enough that they simply could no longer be ignored. Those banned users are very annoyed that VAC has dropped the hammer on them."
Catbots, if you're not familiar with the term, are player-created bots that flood TF2 servers, lining up headshots on everything in sight. They're all called things like 'catbot 1574', and they're a nuisance. But in an attempt to stamp them out, some players are claiming that Valve has crossed a line. Anybody with 'catbot' in their Linux username (yes, not their Steam username), will now find themselves with an automatic VAC ban, regardless of whether they've actually booted up TF2 or not.
Now, I don't know how many Linux users have 'catbot' in their username, but there is at least the potential for friendly fire here. On the GitHub thread where the issue was uncovered, one user said that their Steam account was VAC-banned despite claiming to never have cheated. Another said: "I installed Ubuntu on a virtual machine and named the computer catbot-918 and installed Steam, within an hour of not playing anything I received a VAC ban."
A GitHub moderator for Valve confirmed that the policy was in fact a deliberate attempt to combat bots, adding that it was "not open for discussion on Github" (which, on my reading, doesn't mean that the issue is not open for discussion at all, just not on GitHub).
Valve does have a responsibility, and a right, to stop cheaters playing its games. But as a lot of people on this Reddit thread discussing the issue have said, it does seem a bit ham-fisted to ban someone simply because of their choice of Linux username. And besides, it looks like catbot setups have already switched to a different username, which was inevitable. It's probably not the last we'll hear of it.