Problem found:
All mibbit users use the same IP. Therefor, whenever we ban a mibbit user, we include their ident in the ban. (mibbit users cannot change their ident, and their ident is unique for their IP. This only applies to mibbit users.)
However, mibbit seems to have changed IP, so when we banned someone rude from the channel yesterday, we didn't notice it was a mibbit user, and banned his complete IP, effectively banning all mibbit users.
The new mibbit hostmask is 6af785b7.ea592a9c.com.hmsk
It should go without saying that mibbit users are of course unbanned now :)