Don't the Iraqi people have the right to choose the form of government
that they want?

You bet!

Separation of religion and state is a western ideal, but is not Islamic.
Islam is a way of life, and governs all aspects of life, both religious
and civil. I don't think we should even try to force our form of
government on them, let alone insist on a government friendly to the USA.

Agreed. Democracy or Theocracy, it's their choice. However, a Theocracy (and
a closer association with Iran) would not serve the interests of the current
US administration.