Is it obligatory for the congregant to perform an extra rak'ah after the Imam finishes if he doubts having recited Al-Fatihah, while he believes it to be obligatory, or is he permitted to contravene what he holds to be sound?

The congregant's recitation of Surat Al-Fatiha behind the Imam is a matter of scholarly disagreement. The preponderant and authoritative view is that its recitation is obligatory. If the congregant doubts having recited it after bowing, he must perform an additional rak'ah after the Imam concludes the prayer. It is permissible for the congregant to adopt the view of the majority of scholars, who do not consider the recitation of Al-Fatiha obligatory for the congregant, because a common person is not required to adhere to a specific madhhab in matters of scholarly disagreement, provided that this is not merely a pursuit of concessions. As for those capable of critical examination and scholarly weighing, they are not permitted to deviate from what they have found to be preponderant.