The right is calling them "free speech" rallies because the mayor canceled an earlier one, citing threats of disturbance by leftists.
"My main concern is that they are coming to peddle a message of hatred and of bigotry," Wheeler told reporters, referring to organizers of the two rallies.
"They have a First Amendment right to speak, but my pushback on that is that hate speech is not protected by the First Amendment to the United States Constitution."
The ACLU of Oregon, in a tweet on Monday, said: "The government cannot revoke or deny a permit based on the viewpoint of the demonstrators. Period."
"We are all free to reject and protest ideas we don't agree with. That is a core, fundamental freedom of the United States," the ACLU said.
Founded by Communists and fellow-travelers, the ACLU has a long history of defending the free speech rights of organizations and people hated by the left such as the American Nazi Party and the KKK.