In my opinion you have to go through a conversion to Judaism
Ju·da·ism ( P ) Pronunciation Key (jd-zm)
n. 1. The monotheistic religion of the Jews, tracing its origins to Abraham and having its spiritual and ethical principles embodied chiefly in the Hebrew Scriptures and the Talmud.
2. Conformity to the traditional ceremonies and rites of the Jewish religion.
3. The cultural, religious, and social practices and beliefs of the Jews.
The Bible has this to say.
Romans 2:28-29 says it all.
A reason it would matter is if you ever wanted to immigrate to Israel. When Israel was formed, they decided to grant every Jew the ability to automatically claim Israeli citizenship and move to Israel (the Law of Return). This is called aliyah and has certain benefits associated with it. To determine who is a Jew, they use the mother rule (or conversion). There are some minor conditions like you can’t be practicing another religion or have carried out actions against the Jewish people. It doesn’t mean you wouldn’t be allowed to move to Israel if you aren’t Jewish, but it would make life a lot easier and give you some special privledges. If you were female, it would also determine obviously whether your kids could make aliyah.
Another place where this becomes important is if you ever decide to marry an Orthodox Jewish girl. If you are Jewish, then you wouldn’t have to undergo a conversion to be married in an Orthodox ceremony. Some of my friends ran into a similar situation: her mother had converted in an apparent Conservative conversion. The Orthodox rabbi refused to acknowledge her as Jewish, despite a life of Torah Day School, Jewish camps, synagogues, a bat mitzvah, and so forth. So they got married by a Conservative rabbi. Years later, another Orthodox rabbi vouched for her mother’s conversion (he was the only one doing conversions around here), so poof! she’s a recognized Jew again.
There are other minor advantages, but none that I can think of that don’t require attendance at synagogue or a religious ceremony like a wedding (i.e. witness on a wedding contract or part of a minyan, etc.)