Sounds like they selected this venue merely to make an issue of their announced identity. That's not too cool.
Like the gay couple who selected a baker in Colorado, expressly because they knew he would decline to bake them a wedding cake (although he said he would serve them in other capacities). Looking to cause a problem, in my view.
I've seen some fairly obnoxious college Republican protest and stunts, but on the other hand, they may have a point. It's not clear they were there just to make an issue of their identity. They may well be there to make an issue of institutional bias; a real issue at many liberal college campuses, where being conservative is frequently identified with being racist, sexist, homophobic, etc. (And to an extent it has been even before Trump).
It is not like the gay couple in CO at all; the gay couple had no prior relationship to the bakery, but these students are already involved with Fordham. It's also not like that case because the gay couple were not refused because they announced their identity, but because they wanted to insist on a political message on the product, whereas these guys were not asking for a coffee served in a cup with conservative slogans. If the coffee shop really has a history ("an unwritten rule" as was said) of not allowing conservative students, then it is the coffee shop who made an issue of their beliefs first.
Besides, from the article, "Fordham University released a statement saying that the college itself has no safe space policy, and does not have one that excludes members from the Fordham community to public spaces on the basis of their political views." Seems like the coffee shop manager may be setting policy above her rank.