I agree with everything you wrote except this:
"Wheaton was not only within their rights to fire him, but since he went public with this issue in an apparent attempt to embarrass the college, I would suggest that they should sue him for breach of contract."
That really would depend on the terms of the contract and I doubt that constitutionally any institution could maintain an action for breach of contract over a refusal of an employee to maintain certain religious beliefs, but I suppose its possible, say in the event that the professor had received some value beyond simply the agreed value of his services, like a signing bonus or some such benefit which hadn't been fully "amortized".
I'm less interested in the legal question of whether Wheaton can fire him (that is assumed; no one has argued otherwise). I'm more interested in the question of whether Wheaton should have fired him because he is not an Evangelical Christian, but rather a Catholic Christian. Personally, I think it was a huge mistake for a school that wants the reputation of the "Evangelical Harvard."
If I were the the employee's counsel, I would argue that this contractual requirement was contrary to public policy and therefore unenforceable by the court. I'd probably win, too.