What he is doing is not illegal but rather a really crappy thing to do.
Only if such a petition was sent to the network. Having the government intervene to cancel his show would be just as bad.A more rational petition would be one demanding that his show be cancelled(and that petition might have legs if his ratings are as bad as some have claimed).
Petitioning the government doesn't break the law either. You have right to peacefully do so. That doesn't mean the content of the petition is noble. In this case it is not. If the administration did try to deport him via this petition then hopefully the courts would put a stop to it.
Both sides here are trying to use their civil rights to undermine the civil rights of others. Neither is particularly ethical.