What determines if an action is halted, versus allowed to continue while the action takers are being sued?

As the title. Why are some things allowed, e.g. the modifications to the wh east wing, while others are halted e.g. some states redistricting plan?

Also, why is the law so weak as to be frequently weilded as a strategic weapon/ shield if youre sufficiently well connected? Same can be asked of religion, actually.