Any employer faced with this kind of behaviour and anticipating firing the employee as a result is well advised to go through due process. That includes investigating the allegations, giving the employee the evidence and inviting them to a disciplinary hearing and allowing them to explain their position, then considering mitigating factors (length of service, previous record, whether the post was deleted, remorse, etc.) before finally offering them a right of appeal.
This all takes a while, as you can imagine, but failing to follow a fair process like this can mean a dismissal is found to be unfair at a tribunal even if the underlying conduct was serious enough to warrant dismissal. The reality is that most successful tribunals brought by employees are successful because the company hasn't followed the correct process.
So I am happy for the university to take their time and get it right before firing this man for his obviously vile posts.