Converted Jews

Question

Hello Rabbi, This may sound like a silly question, but I have been confused about something as of late. How many generations must pass before a converted jewish family is accepted in to the Syrian Community. While my parents are Syrian I didnt grow up here and I am new to many customs and rules, such as that of "not accepting converts." Also, would I be wrong in taking a visiting friend of mine, whos parents converted when he was young, to a Syrian shul on Shabbat. Thanks