Obviously, there's merit to protecting historic homes. The only issue here is that, in order to be eligible for the exemption, the homeowner is supposed to make sure that the public has "visual access" to the property, i.e., that regular people can see and appreciate it. In the case of the house being used by the Obama entourage, that requirement apparently is not being met.
Somehow, it does seem to smack of hypocrisy. The house being used by the entourage of an enthusiastically pro-tax president -- who routinely denigrates those who want to keep more of their own money -- apparently isn't even in conformity with the rules that legitimately create a tax break.