Is it permissible to pray behind imams whom the ruler orders to emulate the Shafi'is in their prayer, believing in the sunnah of qunut in Fajr, and prostrating for forgetfulness when forgetting it?

It is not from the Sunnah to perpetually perform Qunut in the Fajr prayer. However, praying behind someone who performs it is valid. If someone who does not perform Qunut is found, praying behind him is more preferable, in adherence to the Sunnah. Scholars have agreed on the validity of the prayer whether the worshipper performs Qunut or not in Fajr. The follower should follow his Imam in matters where ijtihad (independent reasoning) is permissible. So, if the Imam performs Qunut, the follower performs it with him, and if he omits Qunut, the follower also omits it.