If you measure respect in Hollywood by awards...Nicole Kidman and Geoffrey Rush both have Oscars, and Heath Ledger was nominated for Brokeback Mountain, a critically acclaimed film.
Australia has given Hollywood a huge pool of talent--in addition to the above you can add Cate Blanchett, Russell Crowe, Hugh Jackman, Mel Gibson, Peta Wilson, Anthony LaPaglia, Radha Mitchell, Guy Pearce, Poppy Montgomery...and many more.
To some extent, Hollywood is an international business with an LA zipcode. Every project is gauged on how well it will do overseas--investors, producers and directors themselves may not necessarily be Americans, although the finished product is considered to be an American film.
Foreigners in Hollywood are probably measured by the same yardstick as ANYONE in that industry--by their box office gross or TV ratings. There are always going to be sour grapes among the hundreds of actors who lose out for any given role--I don't believe that resentment by American actors is based on any sort of patriotism. If anything, you tend to hear the reverse: criticisms of Renee Zellweger playing the role of Bridget Jones, Kevin Spacey taking on the directorship of the Old Vic Theatre in London, Reese Witherspoon in Vanity Fair, Gwyneth Paltrow in several English costume dramas, etc.
In fact, I can only think of one instance of an English-language film in which there was a requirement that all the actors were of the same nationality: all actors in the Harry Potter films must be English.....however, the directors have included an American and a Mexican.