Religious folks of many types are fond of that saying added as a condition when they ask you to consider their ridiculous propositions. I've heard it from Mormons concerning "asking God to give a sign to let [me] know that [their] religion is right." I've heard it from new-agers concerning so-called psychic readings and other such woo. And I've heard it most recently in the letter posted by Pope Ratzy regarding pedophile priests.
It seems to me this is just another religious equivalent of "have an open mind" wherein the phrase "open mind" = "do not apply logic or rational thought here." In other words, "Don't think about it, just believe!"
Related to the quote from the Mormon stated above, the person claimed to have once "not believed", but then prayed for god to give a sign and she got one, and then implored me to do the same (as stated above). What she failed to realize is that because I truly do not believe, I have no reason to expect an answer and therefore will not interpret random events as "answers from god" which IMO is exactly what she did in her account of her own "crisis of faith." Again, if you believe already or really want to believe, you will find reasons to do so - like interpreting random events as messages from your almighty sky fairy of choice. (I didn't bother pointing out the very obvious "coinsidence" that the "God" which revealed itself to her as being "the right religion" was the very religion she'd been brought up with and indoctrinated in since birth.)
Anyway, to sum up, I just really hate phrases like "with an open mind/heart" or "in the spirit of Faith," because I see them as requests to suspend all rational thought/judgement, which is exactly how religion worms its way into unreflective minds.