Is a person born to non-believers and later converting to Shia Islam considered illegitimate if their parents did not have a formal marriage due to the societal norms in their community?
The Hadeeth from Imam Jafar Al-Sadiq (AS) says: Every community who differentiate between marriage and fornication, their marriage is lawful. كل قوم يعرفون النكاح من السفاح فنكاحهم جائز . (Al-Tahtheeb; 7:475).
The marriage between non Muslim parents according to their society is valid and you are not an illegitimate.
Wassalam.