The common ground of a “mere Christianity” cannot be allowed to become a lowest common denominator.
Here C.S. Lewis is worth heeding. The man who coined the term “mere Christianity” also warned against its misapplication and abuse:
I hope no reader will suppose that “mere” Christianity is her put forward as an alternative to the creeds of the existing communions—as if a man could adopt it in preference to Congregationalism or Greek Orthodoxy or anything else. It is more like a hall out of which doors open into several rooms. If I can bring anyone into that hall I shall have done what I attempted. But it is in the rooms, not the hall, that there are fires and chairs and meals. The hall is a place to wait in, a place from which to try the various doors, not a place to live in.
Similarly, believers who inhabit the various rooms can enter the hall for the sake of dialogue and mutual support. But they cannot afford to remain there, chatting and cooperating and maybe even throwing up some tents, while their own rooms fall into neglect. A conversation has to reach conclusions in order to actually stand for something; a community has to define itself theologically in order to be able to sustain itself across the generations. In an age of institutional weakness and doctrinal drift, American Christianity has much more to gain from a robust Catholicism and a robust Calvinism than from even the most fruitful Catholic-Calvinist theological dialogue.
—from Bad Religion: How We Became a Nation of Heretics by Ross Douthat, Conclusion: The Recovery of Christianity