This is a myth ...A R Rahman's father R K Shekhar (R. Kulasekhar) was a Hindu. He came from a family of reputed Harikatha exponent i.e. Rahman's grandfather was Rajagopala Bhagavathar (Bhagavathar - one who sings bhagwat Gita). R K Shekhar himself was a carnatic music proponent and a harmonium player and was a music director himself. (worked with legendary Illayraja and Yesudas)
A R Rahman's father married a muslim lady, Kareema Begum who converted to Hinduism and took the name Kasturi. She ran away from her home and married R K Shekhar for love and they got married in the famous Thirupathi temple.
They had 3 daughters and 1 son Kanchana, Dileep (later Rahman), Bala and Israth.
A R Rahman learnt his first music from his father playing the piano at the age of 4, but he sadly he died when Rahman was 9 years old. Rahman was then forced to support his family by virtue of being the only male in the house and started working when he was 11 years old.
His religious crisis came when his sister fell seriously ill and who they believed was cured by a pir which triggered his conversion to Islam. Rahman in his interview has said 'As Dileep I had an inferiority complex. As A. R. Rahman I feel like I have been born again.’ ......(...why did he feel inferior as a Hindu?)
His sisters initially resisted conversion, but once he became Rich and famous, his sisters also converted (they dint have much education due to poverty).
Once Rehman became rich, His eldest sister Kanchana who married a Hindu (as she was a hindu) also converted to islam and divorced her husband and left her son. Her son, G.V. Prakash is now a famous music director too. She is now 'Rehana' (..after Rehman). Sadly his other sister Israth is also divorced now.