Real Muslims will never consider a new Muslim as an outsider. History of the Prophet (SAWA) and Ahlul Bayt (AS) proves that they were dealing with new Muslims as real Muslims and sometime better than some born Muslims who are less in practicing Islam. We need to explain to those weak Muslims the real teachings of Islam which are based in true faith and sincere practice and not on the previous history as the Hadeeth say: الإسلام يَجُبُّ ما قَبلَه Becoming a Muslim omits what's before it.
Wassalam.