As a non-religious person, my intuition is to extend the argument that is being made by some Americans right now. "9/11 was perpetrated by religious extremists. If you're going to block this facility, block all religious facilities within a certain range of ground zero." Lumping all religions together is really no different in my eyes than lumping all Muslims together.
On the other hand, the emotional reaction to this is real. Some people are deeply offended at the notion of this facility being built, even if that emotion is being created and fed by mainstream media. While I believe that the builders are well within their rights to build the facility, they should probably factor the feelings of others into their decision. If this is truly intended to be used as a center for religious outreach and mutual understanding, then continuing with plans to build it in the current climate would seem to be counter-productive. Perhaps the right thing to do would be for them to politely change their plans. "We believe that we have the right to build this facility, but we do not wish to cause more pain to the people who are clearly upset by it. We are therefore withdrawing our plans and instead will build the facility on (some other land that we've scrambled to find.)"
What I predict will happen if the facility gets built: it will be the target for Christian extremeists and Christian terrorists. I will go out on a limb and predict that the mainstream media will not call them Christian extremeists, and they absolutely will not use the words Christian terrorists.