There is the definition of a Jew,
and there is the definition of Judaism.
Conservative, Reform, and Reconstructionist “Judaism” are not Judaism. They violate the Torah. They are different religions.
Therefore, their “rabbis” are not Rabbis. Their “conversions” are not conversions and are invalid.
Please see:
http://truejews.org/Igud_Historic_Declaration.htm
A Jew is defined only by one of the following:
1) Someone descended matrilineally from our forefather Yaakov.
2) Someone descended matrilineally from a female who has undergone a Kosher conversion to Judaism.
3) Someone who has undergone a Kosher conversion to Judaism, which includes belief in G-d, belief in the divine origin of the Torah and in its Mesora down the generations, belief in the 13 fundamental principles of Judaism, belief in ALL of the Torah – both the Written and the Oral, and the belief in every single one of the 613 Mitzvos and their performance.
If a Jew C”V performs a sin, he is a Jew who has given in to his Yetzer Hara and performed a sin. His status is that he is still a Jew. However, the performance of certain sins (which the Jew continues doing and which he does not repent of) may cause him to lose the privileges of a Jew (e.g. being counted in a Minyan), while he still retains the responsibilities of a Jew.
Judaism is defined as following the beliefs and rules of the Torah and performing the Mitzvos.
Telling a Jew that he or she can eat Trayf, violate Shabbos, practice homosexuality, marry someone non-Jewish, not practice the Family Purity laws, and act and dress immodestly is not practicing Judaism.