I don't think it's a lack of tact or ignorance. I think they genuinely don't believe that their particular religion is to blame in any way for what happened, and wish others to see it their way.
I can wish for a million dollars, if I expect it to just happen I'm ignorant or stupid. They can wish for others not to see it the way many do, but its not going to happen magically from wishing and actions like they're taking aren't going to help it either.
When I use ignorant in this case I'm actually not necessarily speaking of "ignorant = stupid". It could very well be that they are literally IGNORANT of what many Americans think and feel, as in they do not have the knowledge to know it or to be able to empathize and grasp it.
I also haven't see any evidence that they're lying about their intentions.
For me its a matter of logic that only 1 of 4 things could possibly be true.
1. They're absolutely oblivious. Somehow, someway, they've paid no attention to all the outrage, never told anyone about this prior to it that expressed any annoyance or outrage at it, never took a moment to think "how will people react", and basically went through the entire process completely insulated and with no outward thought and thus thinking they'll "build bridges".
2. They're ignorant to what many Americans think. If anyone they've talked to expressed outrage or anger over this, they figured it must be a minority type thing. They figure they know their religion isn't all extremists, so everyone else must think that. They think islam had nothing to do with 9/11 and it was all about politics and people, or that it had something to do with it but wasn't a cause for it, and everyone else must think that way so why would they care that a mosque is there. They think all the reports of people upset with it is just the media hyping it up. Essentially, they completely and utterly lack the empathy or knowledge of many Americans to understand how big of a tragedy this was to people and how much Islam is tied to it in the minds of many. As such they figure people will have no issue with the place and come and they'll "Build bridges".
3. They're stupid. The same issues as above, only instead of thinking everyone agrees with them or not realizing people who are complaining are a minority, they just figure that ultimately they'll all just come around and realize how great the place is and love it and that all these angry people will really be able to have a bridge built to them. Something I think unlikely, as I believe many are like me and the very nature of how this is being built and where basically assures I'll never go.
4. They're lying. The same issues as above, only they fully realize most of the people who have even a mildly negative reaction towards Islam in general following 9/11 will likely not want anything to do with the place and be amazingly upset, but realize that the notion of "building bridges" will make those that have no issue with Islam think they're sincere and essentially win them over as soldiers in the fight against those condemning the place.
That's the ONLY answers I can figure out.
It can't be that "Maybe they don't care, they just want their mosque there" because if that was the case it doesn't explain their notion of saying its there to "Build Bridges" because if that was their intent they SHOULD care, so stating they don't care assumes their either assumes their ambivalent/ignorant/stupid/lying.