He did get due process.
I don't think you understand what due process is. Generally, unless there's a specific reason, bar complaints like this are run similarly to any court proceeding. People can testify, produce evidence, etc. Due process doesn't necessarily mean it has to take place in court, and since Eastman isn't charged with committing a crime in California, he is in a half dozen other states though, the California bar is taking steps to discipline him due to his conduct. So yes he has had his day in court and they still recommended to suspend him, which is on hold pending his appeal. If there was no due process involved, they wouldn't wait.
Him being charged with several felonies in various states weighs heavily on this because he violated ethical and professional conduct. So even if he manages to escape being convicted or pleading guilty, the bar still believes he acted improperly and will take action to discipline him because of his conduct.