Artistic license (Russian): to my knowledge, there is no Russian word that maps to ‘crusade’ in the sense of a weighty endeavor (as opposed to a religious war) more closely than related English words like ‘undertaking’, ‘campaign’, or ‘struggle’. ‘Red Banner of the People’s Struggle’ doesn’t sound as cool, though.

I suspect this is for several reasons:
1. The Orthodox Church never did crusades, so it isn’t woven into the cultural fabric.
2. The only undertaking likely to be labeled ‘crusade’, the Revolution, would have explicitly objected to the usage of religious terminology.
3. Russians aren’t given to look too optimistically on big, weighty undertakings.

The more you know!