The study of the interaction of governments with their people and other governments is possibly even more difficult than Science and Mathematics. Understanding the principles outlined by Machiavelli may not be as "rigorous" as the pythagorean theorum, but it is jsut as important. It's possible to suggest that politics is more complicated because of its unpredictable nature. Predicting political outcomes requires analysis of people, not just numbers. People are less predictable than a Carbon Atom. This is why it is just as challenging.
I personally think that it is not private education, but public education that is the problem. The Federal Department of Education creates top-down mandates that take power away from the teachers and local school districts. Private education is one of the few places that sill allows for innovation and creativity. A voucher system should be adopted.
This day in age is all about equality and equal education to all, and I believe all should learn about the same topics because they are all so important. Politics is obviously extremely important today, and should not be held as any less important than mathematics, or any field around science.
While people credit science with advances in medicine and technological convenience, we have reached a point in human history when the so called advances in science are threatening our existence, from the nuclear bomb, to technologically induced climate change. The humanities give a small space to the notion that science alone should not govern us. Credibility must therefore be maintained for academics that stand outside of the paradigm of pure science.
Covering humanity issues such as politics and religion are important but I don't think they can be taught without a personal bias.. That being said, not all subjects of math and science should be required. Instead lifestyle skills such as time management, money management, career development and mental health should be covered.
Science and mathematics are what make the world go round. They are what describes our world at the fundamental and physical level and are forever changing to correct themselves. Politics and religion are the polar opposite of this, full of falsities, biases, and even hatred. They are by no means equal.