Whose cultural values would be taught? I'd guess that the majority of the US doesn't share your particular social values, not to mention how much those values have changed over the last 20 years (e.g. on things like gay marriage as an obvious example).
Regarding values: An emphasis would be placed on Constitutional values, with an intentional focus on ambiguity and how the Constitution has/has not changed over time. Slavery and civil rights would be a fascinating topic to cover through this lens.
The goal should be training new citizens to be unbiased critical thinkers by exposing them to a flood of new ideas while teachers emphasize socratic questioning, debate, communication skills, research, and related skills (eg statistics). Disagreement is absolutely fine, that's the American way... as long as students have the tools and mindset to effectively research and debate new ideas, with the humbleness to change positions.
Ideally, education also would involve a mandatory exchange program to expose students to other lifestyles and subcultures while continuing to work through their school program.
