Ah yes, but hypocrisy is the human disease after all...
I think that it all came down to expediency in the end, the Klingons where their allies during the war and any action that they took was justified in hasting the end of a long bloody war. And since the Eleventh Order was technically a military order, why not brother?
After all, they where only Cardassians.
Plus the feds tacitly condoned genocide, (albeit againist a ruthless amoral bunch of xenophobic mass murderers) so its either a moral defect, coldblooded pragmatism or as those arrogant Rihannsu would have it, the humans are one of the most devious races you could ever hope to encounter.