The people voted for this though. The secular dictatorship was replaced by a democracy, and this is something Sunni and Shia parties agree on with a majority in the parliament. The old (abolished) law was introduced in 1959 with the beginning of the republican era after the end of the monarchy in 1958.
Even the opposition to it doesn’t look that popular, not a lot of people:
The US put Iraq through sanctions, killed its scientists, and artists, and then invaded it and destroyed its infrastructure. The majority of Iraqis left through all that trauma had nothing but their religion institutions and tribal connections left, and through the democratic system the US imposed voted for this directly or indirectly. It sucks, but the destruction of Iraq started years ago.
No, it is a parliamentary democracy.
A democracy is never a guarantee of favorable or progressive outcomes.