Chun didn't "get in the middle of the exemption process." The WSU process was that a committee evaluated the applications for exemption. This was designed to be blind, without identifying information attached (although, if you were a high profile position who waited until the last minute, and then notified the press when you applied and your basis...that probably degraded the anonymity). If the committee felt the application met the requirement, they referred to the supervisor to determine if an accommodation could be made based on the job duties.The State was incredibly vague about how exemptions would be granted or who had the authority to grant them. We had to deal with out where I work. It was a total cluster.
My understanding is that Rolo's application for exemption was determined to meet the requirements to provide an exemption, but that Chun - as his supervisor - determined that he could not be accommodated.
IF that's the case, most of his lawsuit is DOA. He had due process, the same as any other employee, which eliminates the 14th amendment claim. The 1st amendment claim and religious discrimination claims against Inslee, Washington, and WSU fail, because they didn't make the decision. It remains against Chun (although he'll likely be dismissed as a defendant because he was acting as an employee), but it's going to be nearly impossible to prove that case - especially when Chun is also Catholic. The breach of contract claim depends on the exact contract terms, but could backfire on him since I'm sure there's a clause about representing the university positively. The civil rights violation probably fails early too, since nearly all existing case law says that state and local authorities do have the right to impose vaccination requirements...and has Supreme court precedent (although...not by this court, and it's hard to predict how they'll act).
All of the talk about whether the mandates should have existed in the first place is irrelevant. They did, and WSU had to enforce them. The only real decision to be evaluated is whether Rolo was unreasonably treated in a manner different from other employees. And, it doesn't appear that he was.