Reform Judaism has recently extended the definition to include some children of a Jewish father who practices Judaism. Already-circumcised males undergo symbolic circumcision. Studying the basics of Judaism is a necessary precondition for conversion. Minor children can be converted, but can opt out upon age twelve or thirteen. Rabbis often discourage conversion to Judaism, as a matter of policy, but this is not usually the case for someone who is part-Jew or married to a Jew.
Many Syrian congregations reject converts.
Orthodox Jews do not necessarily recognize conversions performed under the auspices of other branches. If the conversion out of Judaism was under duress, this does not apply. One who is matrilineally of Jewish descent, but was raised as a non-Jew, is to be treated as a Jew under Jewish law. From the Jewish point of view, baptism itself has absolutely no impact on one's status. They are treated as Jews under Jewish law.