I have no major gripes with Reince Priebus in general, but it seems in this instance he committed a fireable offense by interfering with a Justice investigation. Especially in light of what happened when then-AG Loretta Lynch met with Bill Clinton aboard his plane last year, which was a less serious situation given that we do not know if anything improper was discussed. She recused herself from the email investigation at that point.
I hesitate to say Priebus has to go because my guess is he is a moderating influence in contrast to Steve Bannon, who wants to deconstruct the federal government. But he broke federal rules and maybe the law.