Progressive atheists and progressive theists certainly have common ground for social action, but how do they put aside their differences without alienating their members. Antitheists will be naturally conflicted over accommodationism, but what articles of faith will theists have to renounce in order to resolve their cognitive dissonance over working with atheists? The term "Interfaith" already suggests a rejection of sectarianism. That's a good start.
While the term "Interfaith" suggests a rejection of sectarian division, it also implies theonormativity. To work as equals with atheists, the theist must reject the notion that faith is a virtue in its own right, that doubt is a moral failing and that worship is commanded. What remains is a god that doesn't require praise, or even acknowledgement.
Suppose an Interfaith activist manages to find inspiration in an indifferent god. Are there other impediments to respecting atheists as equals? Even some of the most non-theistic religious rationalists will assert that religion, at least for them, is the route to ultimate meaning. How does one assert that religion is necessary for one's own personal discovery without implying that the non-believer is oblivious to the inherent value of religion? The religious rationalist may be able to suppress the need to express these ideas to avoid offense, but cognitive dissonance is not relieved by keeping one's thoughts to oneself.
Even secularism can be a source of unspoken controversy. Putting civil law above cosmic wisdom would seem counter-intuitive to one who believes in religious morality. To the fundamentalist, God's judgement is sufficient to render an act moral or immoral, independent of any virtue or vice inherent in the act itself. To arrive at secularism, the believer will have to accept, at the very least, that God's judgement coincides with what is true because God is wise.
But if religion were truly the source of all morality, why shouldn't it be the law of the land? Is it enough for the believer that other religions have missed the mark on moral questions to see the necessity of secular government? Perhaps the religious secularist is compelled by the idea that reason and cosmic law will inevitably converge on the same conclusions. History suggests otherwise.
A theist's cognitive dissonance is not the responsibility of the atheist, but it does present a compelling philosophical question. The religious Interfaith activist will have to accept a number of heresies to work as equals with atheists. These heresies include an indifferent god as well as meaning and morality independent of religion. More likely, religious Interfaith activists will have to suppress the urge to opine and leave their cognitive dissonance unresolved. This is perhaps the best state of affairs that one could expect. After all, wouldn't resolving the cognitive dissonance ultimately lead the believer to reason?