Those who are following BZ’s post about the Syrian community’s alleged refusal to accept properly converted Jews (which is itself, at least one, if not several, violations of halacha) might want to take a gander at Gil Student’s post on Hirhurim, which has a letter refuting the charge from Rabbi Moshe Shamah.
The gist is:

That Edict was enacted to discourage community members from intermarrying with non-Jews. It acknowledged the reality of the time that conversions were being employed insincerely and superficially. Accordingly, conversion for marriage to a member of the community was automatically rejected…
…I quote from an official formulation of the Sephardic Rabbinical Council of several years ago that reflects their position: “1. A conversion not associated with marriage that was performed by a recognized Orthodox court – such as for adoption of infants or in the case of an individual sincerely choosing to be Jewish – is accepted in our community. 2. If an individual not born to a member of our community had converted to Judaism under the aegis of an Orthodox court, and was observant of Jewish Law, married a Jew/Jewess who was not and had not been a member of our community, their children are permitted to marry into our community.” Based on these standards a goodly number of converts have been accepted into the community. Genetic characteristics play no role whatsoever…
the quote claiming that even other Jews are disqualified from marrying into the community “if someone in their line was married by a Reform or Conservative rabbi” is a totally false portrayal of community rabbinical policy. Many Ashkenazim whose parents were married by such rabbis have married into our community.