Many people promise before marriage to embrace Islam or Shia Islam after marriage, just to get married with whom they want to marry, but they fail to fulfill the promise after marriage especially after passing years after marriage or after matrimonial misunderstands which are usual between couples. You must be sure the non Shia girl who wants to be married to you is really ready to follow Ahlul Bayt (AS) not for the sake of marriage but for the sake of Allah to a follower of Islam of the Prophet (SAWA) and Ahlul Bayt (AS).

Your parents might have this concern and don't wish to see you in trouble in the future.

'If this girl is ready to follow Ahlul Bayt (AS) for sake of the Truth, she should start following Ahlul Bayt (AS) now and not wait. That should indicate her intentions and might help your parents to believe that she is a sincere person in her promise.

'Wassalam.