I find all the head lines "Married archbishop rejects Vatican’s excommunication" to be rather dumb. Exactly when in the history of the Church did anybody ever accept an excommunication? It makes it sound like excommunications are served like subpoenas, except with a yes/no block on it to be filled out as to whether you accept it or not. People are excommunicated in the first place because there was something wrong with their judgment, so whether they accept it or not just does not matter.
Now there have been plenty of those who were excommunicated and in a way did accept it. They came to see that they were wrong and repented of their disobedience. You have to wonder though in the modern climate just how effective an excommunication is compared to in the past. It is not exactly a mark of Cain to many people and might even be considered by some as a reason to approve of a person. It is harder for someone to repent of a sin when they are supported by so many.
News coverage has often be laughable in describing excommunication as kicking somebody out of the Church or as a declaration that somebody is no longer Catholic or within the Catholic Church. You won’t hear that it is a medicinal and spiritual penalty that bars a person from the sacraments until they have repented and the penalty has been lifted.