Hence my mention of the need to tailor their request. Obviously they would need to assert some sort of criminal activity connected with the protest to get a warrant, but it's not as if cops are unfamiliar with amplifying or even provoking such, and exaggerating the level of danger in their warrant application.
This might seem like a cynical take, but you can see stories almost weekly of border patrol officials admitting to lying about claims of criminality; here are two recent examples: