My entire family had a conservative conversion. We attend a modern orthodox shul. We don’t keep kosher and we drive to shul on Shabbat, but our kids attend a Hebrew day school, we go to services every week, and we observe all holidays. I know there are people at shul who won’t accept our conversion regardless, but is there any precedent for my kids to have an orthodox bar mitzvah?
It is written in the Talmud (Tractate Bechorot 30), Maimonides (Isurei BIah 12-17), and in the Jewish Code of Law (Yora Deah 268-1,2), that there are three requisites for a conversion to be valid. The first one is that the convert accept upon him/herself all of the commandments of the Jewish religion. Judaism is not merely a religion in theory, but a way of life, and becoming a convert means that the convert accept to “convert” his way of life to the Jewish way of life, which means living by the laws given to use by G-d. Without this basic acceptance the person essentially is saying that he wants to be called a Jew when essentially he doesn’t want it as his way of life. Accepting to do the commandment means following the Jewish Code of Law, which is a compilation of the laws written in the Talmud etc. If the conversion was done without accepting to keep kosher, Shabbat, laws of family purity etc., then the conversion is unfortunately not valid, and the potential converts are the same as they were before the invalid conversion. Regarding having an orthodox bar mitzva, if a child ifs not considered a Jew he may not get called up to the torah or lead the prayers, but as far as having a social party, I don’t see an issue with that.
Additional sources Ahi Ezer 3-26, Igrot Moshe Yoreh Deah 3-106,108, Lehorot Nossan 3-83, 5-62, MInchas Osher (Shabbos) 34.