Since the Blades were the Emperor's protectors before becoming dragon hunters, it would also be honoring the history of the Blades to side with the Empire.
Wasn't it the opposite? They served Tiber while we was Dragon born, and then when he became emperor. They served his family because they to were Dragon Born. But, when Martin died there was no Dragon Born on the throne so they quit serving him directly thus fighting more on the front lines.
Since they hate the Thalmor so much, Stormcloaks does make a certain sense, though I imagine they'll join whichever side the Dragon Born does rather readily.
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