You don't just get to ban good behavior to stop bad behavior. The presence of illegal looting does not take away constitutional rights. If it did, the government would have incentive to incite riots and looting to force the breakup of peaceful protest.
I agree to a point, but I do think depending on the scale of the lawlessness that temporary measures such as a curfew can be reasonable in order to avoid large scale destruction and violence
https://en.wikipedia.org/wiki/Strict_scrutiny