High school history is not meant to be a comprehensive summary of American and world histories. It is meant to be a framework to support an umbrella ideology to unify the nation as a whole. Real, critical study of history is something better left to universities and the independently motivated individual. As outright falsification of history is not acceptable, certain parts of American history should be emphasized at the expense of others in the high school curriculum. For example:
Things to be emphasized: Victory over Naziism in WW2, civil rights movement, opening of non-white immigration in 1960s, ties between US and Israel, free trade pacts, NASA, fall of colonialism, importance of technology in american history, importance of individuals of color and Jews in American history, Martin Luther King, FDR, Reagan, & Obama
Examples of things that should be de-emphasized or ignored: Robert E. Lee and other members of the confederacy, reconstruction, black nationalist movement, Washington, Jefferson, and other slave owning national figures, riots, lynchings in the south, Chinese exclusion laws, Japanese internment during WW2, Puritanism, Urban renewal, Trail of Tears, Woodrow Wilson, Vietnam War, Counterculture movement of 1960s, Jim Crow, The American Revolution, The Mexican War, War of 1812, & Philippine Insurrection.
History courses have to reflect the students that are being taught. History cannot be divisive or taught as a series of struggles. People have to be happy with one another as neighbors.
The United States of America is an enormous melting pot of different races, religions, and ethnicities. With an educational curriculum that solely focuses on American history, we are leaving vast historical knowledge out of the minds of our nation's youth. They too should have the opportunity to gain a more in depth understanding of other nations, to reflect the understanding that we are not alone in this world.
Your question is misleading because it almost implies that we should change our curriculum to 'not offend' foreign religious/cultural beliefs that are becoming more prominent in western society. So, if that were the question, my answer would be: No, secularism was a leap in the right direction.
Since your asking whether or whether not the curriculum should be changed to include other peoples cultures because of their roots, the answer is still no. Part of assimilation is learning about the country people move to, how that country came to be and why individuals are moving to it. People can learn about their ancestors at home, or, should their parents decide, find a school that reflects their beliefs better outside the public school system.
In a rare three part answer, my opinion is that the united states curriculum could stand to alter the history curriculum to include world history. Maybe it would be less nationalistic and less politically indoctrinating if that were the case. Ever watch jeopardy? An American can name any presidents secretary of (w/e), but is hard pressed to tell you who Canada's or Mexico's current leader is.
When learning about history we should not change studies and learn about things differently. We should learn about history as it happened and not put any bias into it. To continue to put different bias and perspectives into history simply shows that we are still living in a divided world where everyone is not equal.