Viggo Mortensen, who plays the title character in The Return of the King, has used the publicity platform provided by his role to trumpet his anti-war and anti-Bush views. Since the release of last year's Rings installment, The Two Towers, he's turned up for numerous press interviews wearing a "no more blood for oil" T-shirt and freely offered his bitter critique of U.S. foreign policy.
The article also discusses him making public speaking appearances at ANSWER rallies, etc. That's putting himself forward to the public for purely political purposes.
Rhys-Davies answered a question that was asked of him in an interview. If he started attending Free Republic rallies in D.C., stepping up to the microphone, and making blatantly political speeches, you might be able to compare them more fairly.
That being said, Mortenson has the right to say whatever he wants, and other people have the right to make fun of him for it. I think what people sometimes object to is when a person takes an occasion intended for discussion of an apolitical movie, and uses it as an opportunity to make a political speech. That's why people don't like political speeches at the Oscars.
FWIW, there's nothing improper about Mortenson speaking at ANSWER rallies. He's certainly entitled to speak out on issues just like anyone else. But that also gives people the right to think he's an idiot. And if it affects their willingness to see him in movies, that's their choice. For me, I don't care because I think his opinions are inconsequential. I care more that he was a crappy Aragorn, and that was before I knew his politics.