You asked the question, would I, I understand that as meaning I would still be me, born of the same parents and with the same heritages from all my family. So no, I would not be a muslim, I still would be a Child of GOD. If I were to be born of different parents then I would not be me, isn't that correct.
God loves those who believe and those who do not and the same goes for me, you have no choice in this matter. That puts the matter of total free will to rest.