Suppose there's a communal meal in a secular workplace, at which some of the food is reliably kosher. Now suppose that right before anyone takes any food, one of the participants, to general assent, says grace, including a line like "We consecrate this food to Jesus Christ." Is there any problem with consuming any of the food after that?
There's a rule that "you can't prohibit that which does not belong to you." A pagan can go deify my cow and bow down to it all he wants; he can even slaughter it to his idol; if it's my cow, he did nothing and you can derive benefit from the cow. So the first and major question is, who owned the food in this situation, and who consecrated it? Moreover, what does "consecration" mean? Is that the act of sacrifice, or merely designating it for sacrifice? (The latter wouldn't prohibit it.)
The next question would be how to approach Christianity vis-a-vis the prohibitions related to the accoutrements of idolatry, which is addressed elsewhere.
The third question is whether a declaration of consecration alone (even by an absolute pagan on his own food) is enough to prohibit it. If I recall correctly from the whole mess about wig hair coming from Hindu temples, there are different opinions in Tosfos whether any item used in pagan worship becomes prohibited, or does it have to be specifically the object of pagan libations, bowing, incense, or animal sacrifice. I don't see a verbal consecration in any of those.