Comment 4 for bug 345966

bryen, Juan makes a good point, but there's a missing piece that allows you to do what you want: if you unfollow someone you could open a separate tab and search for "from:username", effectively separating those updates from your Messages.

I do think you'd get better mileage out of an RSS reader for those types of updates though. (And if the user doesn't have an RSS feed driving that Twitter account, shame on them.) :)

Caveat: if you do that, you won't be able to read their updates through another Twitter client, so this would probably only work if Gwibber is your primary/only client. (Thus, I'm changing the status to New instead of to Invalid.[1])

Hope this helps!

[1] (Juan, not sure if you're a developer and/or if your comment was indicating a rejection of this request. Assuming not; pardon if I'm mistaken. :)