How can we stop them from any legal standpoint . They can not stop us either. They can make up all different kinds of stories about us and we would fight back. They have the same rights. Ethically they may be wrong but in this country legal rights are above ethics.
We can not act like them and bring ourselves down to their level. We must show them we are better by tolerating their building of the mosque. Do unto others as you would like others to do unto you.