Holy crusade is pretty religious yes. So why do they not use the emperors holy symbol? These in universe people have no idea what a cross is.
And if they draw from comtemporerly or historic sources, why the Christian crusade? Where are the moons of the Muslims? The hammers of the vikings? The candelabra of the yews? The small fat men? An avatar of the divine? The five pointed star of the ancient onse. All of these would make as much sence.
The moons are on Teclis and friends and the hammers are on the Stormcast in AOS
The Roman Imperial Aquilla is all over Imperial forces.
A cross is a very basic symbol, like a O in Noughts and Crosses (Tic Tac
Its not like its the specific cross (the crucifix) that the Christians use as there main symbol.