The 1st amendment gives a person a right to speak -- it doesn't give them the right to be heard.
The First Amendment guarantees (not "gives" -- that's the leftist perspective on life) the right to speak without being muzzled by arbitrary (i.e. not justified by the protection of other rights) act of government.
Forcing a business to move beyond the range at which a legitimate nuisance argument can be made is a clear-cut example of arbitrary government action.