If it is no surprise to learn that Sean Penn, outspoken leftist actor, is the son of Arthur Penn, an old time Commie movie director, it should be no surprise that Mel Gibson, traditionalist Catholic, reflects the views of his father, Hutton Gibson, associated with the "sedevacantist" faction of traditional Catholicism. His father was skeptical about the Vietnam War; he is skeptical about the Iraqi War. There is no evidence to indicate that Mel Gibson adheres to the "Zionist-Masonic" conspiracy theories or the denial of the extent of the Holocaust that Hutton Gibson holds. However, movies like "Conspiracy Theory" and "Signs" indicate that Mel Gibson is very familiar with conspiratism, even making jokes like having the Hess children wear tinfoil hats in a scene in "Signs."
Children are seldom carbon copies of their parents. Even Sean Penn is probably a less extreme leftist than was his father. OTOH, Jane Fonda's pro-Vietcong radicalism was well removed from Henry Fonda's New Deal era liberalism. Successive generations of Tafts in Ohio politics have grown increasingly liberal. The same likely holds for Mel Gibson vs. his father.