Debate: On what legal grounds could the Ground Zero mosque be rejected?

In a comment to an earlier post, a reader raised a good issue:  Let’s accept as absolutely true that the proposed Ground Zero mosque is emotionally offensive, and that, for Islamists, a mosque at the site of a battleground is the sign of conquest.  Do those two factors justify refusing the mosque on legal grounds, whether those legalities arise from municipal codes, state legislation, federal legislation, or the Constitution?

Debate, please.  I ask only that the debate be polite, since this is a heated issue.  As an aid to the discussion, I offer both John Hawkins’ list of quotations making the case against the mosque and Dorothy Rabinowitz’s WSJ article.