Ideology and religion are somewhat contested and fuzzy terms and their meanings vary depending on whom you’re talking to. The definition of ideology I will be using borrows from Robert Jay Lifton and Willard S. Mullins: an ideology is a relatively comprehensive and coherent set of convictions (a “vision”) about how humans and the world works, which is powerful enough to influence one’s thinking, feelings, evaluations, and actions. In this sense, I consider mindfulness as an ideological movement. As for “religion”, William James and Clifford Geertz will be my guides. In The Varieties of Religious Experience (Electronic Classics Series, 2002-2013), James defines religion as:

“…the feelings, acts, and experiences of individual men in their solitude, so far as they apprehend themselves to stand in relation to whatever they may consider the divine. Since the relation may be either moral, physical, or ritual, it is evident that out of religion in the sense in which we take it, theologies, philosophies, and ecclesiastical organizations may secondarily grow.” (p. 38)

And what is the ‘divine’? Per James:

“The divine shall mean for us only such a primal reality as the individual feels impelled to respond to solemnly and gravely, and neither by a curse nor a jest.” (p. 45)

Now to Geertz's definition of religion.  In The Interpretation of Cultures (Fontana Press, 1993) Geertz defines religion as:

“(1) a system of symbols which acts to (2) establish powerful, pervasive, and long-lasting moods and motivations in men by (3) formulating conceptions of a general order of existence and (4) clothing these conceptions with such an aura of factuality that (5) the moods and motivations seem uniquely realistic.” (p. 90)

Geertz identifies suffering as a specific religious problem:

“As a religious problem, the problem of suffering is, paradoxically, not how to avoid suffering but how to suffer, how to make of physical pain, personal loss, worldly defeat, or the helpless contemplation of others' agony something bearable, supportable—something, as we say, sufferable.” p.104

Geertz further describes a “religious” perspective as:

"… [moving] beyond the realities of everyday life to wider ones which correct and complete them, and its defining concern is not action upon those wider realities but acceptance of them, faith in them. It differs from the scientific perspective in that it questions the realities of everyday life not out of an institutionalized skepticism which dissolves the world's givenness into a swirl of probabilistic hypotheses, but in terms of what it takes to be wider, nonhypothetical truths. Rather than detachment, its watchword is commitment; rather than analysis, encounter. …it deepens the concern with fact and seeks to create an aura of utter actuality. It is this sense of the "really real" upon which the religious perspective rests…" (p 112)

According to James and Geertz, the essence of religion has nothing to do with god(s) or doctrine. At its core, religion is about experience and a conviction about the really real. And it is in this sense that mindfulness is a religious movement.