They are apparently not trying to get the university to drop “Trinity” from the diploma, on the theory that “Trinity” directly references the Trinity, and not everyone believes in the Trinity (one of whose members is Jesus Christ).
But beyond this, the problem with this argument — and the flip side argument that the Constitution is a Christian document because it too mentions “the Year of our Lord” — is that it takes things far too literally. “The Year of our Lord” in a date is about as religious as Providence, Rhode Island, or Corpus Christi, Texas. The meaning no doubt stems from Christianity, as so much in our culture stems from Christianity. Yet all the terms have acquired secular meaning, and using them does not require belief in the theology from which the terms originally stemmed.
I think there are at least two problems with that analysis. First, unlike "Providence, Rhode Island" or "Trinity University", there is another well-known and commonly used term that fills the niche of "A.D.": "Common Era" (C.E.). I have no other clear way of getting someone to know I'm talking about Providence other than by saying "Providence". But while C.E. is certainly less commonly used than A.D., it is quite well-known and part of the English lexicon. Of course, sometimes college names do change (Carleton used to be Northfield College, Duke University used to be Trinity College until 1924), for a variety of reasons, and maybe at one point students will come up with a new name for Trinity that isn't religiously oriented. Which is, of course, their right -- think Phillip Morris to Altrea. If the constituent body of an institution wants to change its name -- for whatever reason -- I don't see why "because the current name might offend some stakeholders" is a particularly bad reason.
But I think the bigger issue is that unlike both Trinity and Providence, "In the Year of Our Lord" isn't just a reference to a religious history, it is a specific religious affirmation. It makes a statement of belief. A place can be named after any number of things, and the religious beliefs of its founders are as good a place to start as any. I don't think anybody reasonably interprets it as holding any normative reflection on the beliefs of its contemporary citizens. By contrast, "in the year of our Lord" has very specific doctrinal message behind it. It doesn't just point to some historical connection with religiosity, it makes a particular claim about the nature of religious truth. That puts it in a qualitatively different field. Even as a resident, it doesn't say anything about me that folks who believed in Christian Providence founded a town in Rhode Island. It does say something when the official documents I receive come with a contested religious claim on them.