guilty for being white / male.
Yes, that was most definitely their offence 
Warwick seem to have acted correctly
Warwick has fucked up, first of all by not simply expelling them, as other universities, such as Exeter, have done (in the Exeter case, the chat wasn’t even about, or intentionally shown to, specific individuals). Then by not applying its penalties consistently, thus allowing an appeal to succeed.
I actually agree with you about mob rule, and that does make me uncomfortable, but the fact that this outrage is happening doesn’t therefore mean that the university is in the right.
I also think there is a middle ground we might like to aim for between the response of a mob and reading a victim’s letter and only being able to understand it in terms of its rhetorical devices.