Mammle
There was a convert who converted in israel, Rav Ovadiah Yosef the Gadol hador for Sephardim flew to Brooklyn to vouch for her and they still would not let her marry in.
(It almost did create a schism because many did not want to disobey the Gadol Hador especially since he flew to Brooklyn to speak to the leaders)
This story was related in a New York Times article about Syrian Jews. The woman who converted was involved in a romantic relationship with a member of the Syrian Jewish community which is probably why they refused to accept her.
According to a thread on iamamother some geirim have been allowed to live in the community, but sincere converts (i.e. who converted for the love of Judaism) have not been allowed to marry Syrians. A comment on the daas torah article claims that a grandchild of one of the signatories in fact married a ger… it seems very unclear. Have any geirim been allowed to marry into the community. Are geirim who are not members of the community but choose to daven there allowed to get an aliyah? Are their children accepted in Syrian schools?