Religion in general plays a very important role in Middlemarch, but the actual form that that religion takes (Catholicism, Anglicanism, Methodism, other –isms…) isn't as important as the internal effect the religious feeling has on a character. We're calling this kind of general religious feeling "spirituality." It can apply to personal belief or moral sense, but not to organized or institutionalized religion.
Dorothea's spiritual life is intense but vague. Because she isn't able to put a name to her spiritual longings, she mistakes the prospect of a marriage with Mr. Casaubon for a spiritual mission.
Mr. Bulstrode's public piety isn't entirely a hypocritical act. He does have an intense personal faith, but he has managed to persuade himself that his previous misdeeds were part of a Providential plan, while the peccadilloes of his fellow Middlemarchers are more condemnable.