I don't think Hollywood is anti-British at all. There wouldn't be so many British actors working in Hollywood films and winning awarRAB if that were the case.
I think what most people are complaining about is the hero always having to be American. I think Hollywood does that to cater to their biggest market. I know foreign grosses are becoming more and more important, but the US/Canadian market is still the biggest film market in the world, and most films will get the biggest percentage of their gross there. Remember, films aren't made for charity. It IS a business. It is smart business practice to cater to your biggest customer.
As for the Patriot, I haven't seen the film, but what else do you expect from a film about the American Revolutionary War? That and the 4th of July Independence Day celebration are big deals in American history. There would have been a big backlash if the rebelling Americans were depicted as the villains. On the other hand, the American Revolutionary War is not integral to British history. I remember a few British posters on another board mentioning that it wasn't even mentioned in their history books. So the British being depicted as the villains of a battle that doesn't mean much to you guys shouldn't be a big deal.
But I have seen a lot of anti-Americanism depicted in British televison shows, especially comedy shows. I think the British media is much more anti-American than the opposite.
The American government never supported the IRA. Individual American citizens were funding the IRA because of their pride in their Irish heritage, not anti-British sentiment.
Also, what is your evidence that Mel Gibson is anti-British? I have never heard this claim. (On a side note, I do agree he is American. He does not and has never had Australian citizenship, although he did live there for a number of years).