Answered by Sidi Mostafa Azzam
Would it invalidate the prayer of a Shafi`i to pray behind a Maliki imam that omits the basmalah in his Fatihah if we were to follow the transmitted position in the Reliance (F12:29). I am not advocating this as the Reliance also quotes Shaykh Nuh Ali Salman (may Allah preserve him) who provides the easier positions of the Hanbalis and Malikis and as the shaykh says about these other positions: How close this is to the spirit of the Law, which strives for Muslim unity.
According to the reliable (mu`tamad) position of the Shafi`i school, it is invalid to pray behind an imam whose prayer you consider invalid (i.e. whose prayer your school considers invalid).
There exists a weaker (though also strong) position in the school that your prayer behind such an imam is valid so long as it is valid according to him (i.e. his school), and you are allowed to implement this position in your own personal life.
What I have mentioned above is the upshot of what the Minhaj of Imam Nawawi and other texts (such as his Majmu` and Jurdani’s Fath al-`Allam) indicate.
Also, Sheikh Nuh Keller asked Habib Zayn bin Sumayt, the mufti of the Shafi`is in Medina the Illumined, a question similar to the one above and Habib Zayn confirmed in his answer that the weaker position is also sound (sahih) and strong (qawiyy), and therefore permissible to implement in your own personal life.
And Allah knows best.