Based on what he wrote - having actually read it - it would appear he is saying that if a Catholic in the employ of a Catholic institution/organization in which public disagreement with the Church by an employee would cause scandal, e.g. a Catholic divorces and remarries outside the Church and THEN engages in something such as public dispute with the pastor of a parish or the local diocesan, the institution/organization would have grounds for firing.

I agree with him on that.

Obviously if your scenario is a state employee, the answer would be “no”.