Unfortunately, you are completely wrong. Many, many conservatives have acted like statist liberals on the mosque issue e.g. they are willing to use any means necessary to stop the owner from building it on his own land. Countless freepers (who proclaim, much like typical leftists, that property rights "are not absolute") have asserted to me that such pretexts as zoning and other violations of property rights be used to ban the mosque.
I would certainly favor the approach of using general public disfavor to dissuade the Moose from building a new complex with mosque on that spot. If it’s really intended as the diplomatic effort which it is being billed as, they’ll respect the public mood and change the location or give it up. If they’re being snotty nosed about it, they’ll reveal that in due time.
You are right. If authority figures told some freepers it is necessary to cut off their heads for the cause of the US military, they would chop chop and haunt everyone who didn’t from the grave as betrayers to the country.