Opposition to Park51 (aka. Cordoba House) reflect the Christianist backlash against Islam extremist in the post 9/11 world of arguably the worst kind.
Below is a summary (and crude generalization) of the various philosophical leaning and their various response against Islam extremist:
Moderate atheist – religious extremism is the problem
Moderates religious sympathizers – Islam extremism is the problem
Anti-Americanism – American Middle Eastern policy is the problem
New atheist – Religion is the problem
Christianist – Islam is the problem
-Moderates of either kind probably have the best intellectual foundation to form a pragmatic strategy against Al Queda. Their response allow them to ally with moderate Islam and isolate extremist in their own society.
-Anti-Americanism response would be for the US to fundamentally change their Middle East, which is probably unrealistic (but I really dont know enough about it).
-New Atheist approach is intellectually appealing and coherent, but they are either insensitive to the spiritual need of the religious or unable to put forward an alternative to satisfy that need (evidently, secular humanism is just not attractive enough).
-Christianist approach lumps Islam extremism together with moderate Islam. It is by far the most hypocritical, tribal(my religion is better than yours) and dangerous response. It alienating moderate Islam and submitting to the clash of civilization narrative favored by the extremist.
If the right wingers are as patriotic and Al Queda hating as they are, they should really have that mosque built. There is really no good reason for the opposing it, except for dubious short-term political gain.