If a non-practicing Jew is still considered a Jew...?

There are many reasons. You will already get plenty of answers to your question.

So, I thought we should consider one question.

If Orthodox Judaism accepts Messianic Jews as Jews, then they must acknowledge that the beliefs of Messianic Judaism are compatible with Judaism.

Messianic Jews keep the Torah. Orthodox Judaism has no issue with Messianic Jews in that respect since they also keep the Torah. Of course, there is still an issue on the authority of the rabbis, but that's another can of worms.

If Orthodox Judaism accepts Messianic Jews, they must also accept that the Jewish Messiah is Yeshua, and the Messiah is God. It can't happen without Orthodox Judaism contradicting the voice of the rabbis of the past.

While Christianity only refers to the religion, being Jewish refers to the ethnic group and the religion. If a person is born to a Jewish mother and/or chooses to follow the Judaism, then they're Jewish. In the example you gave about the Messianic. The Messianic is still Jewish if the mother is Jewish. The fact that a messianic doesn't follow the religion is irrelevant.

As for your second question, being a non-practicing Jew has nothing to do with being rebellious towards god. Some non-practicing Jews follow another god, and some (like me) follow no god.

Firstly- lets address the fact that a non-practicing Jew is still considered Jewish. The reason for this is simple- they have not rejected Judaism in favour of another religion! Until somebody shows their rebellion by worshipping in a nother religion, we give them the benefit of the doubt and still count them as Jewish- after all, we are told to judge others favourably!

when it comes to "messianic jews", the situation is not the same. The vast majority of "messianic jews" have zero connection to Judaism aside from belonging to their missionary movement. A small percentage have a tenuous conneciton but would not be considered Jewish by Jewish standards and something like 1% were actually considered Jewish before converting to "messianic judaism".

The simple reality is, that even if they did have a connection prior to converting to Christianity (whether they want admit it or not, "messianic judaism" is just another Christian sect) once they converted they lost any connection that they had. The Torah is clear in Shmot (Exodus) Chapter 12 v43 that the Jew who converts to another religion is no longer a part of the Jewish community. This ruling is seen in the Talmud in masechta Sanhedrin where it is stated that an apikoros is not counted as a Jew and loses their place in the world to come (in other words, they are punished with kares (spiritual excission)). This same Mishnah is repeated at the start of masechta Avot in the Mishnah. This cutting off in this world and the next is reflected in rulings by the Rema in the Shulkhan Aruch (Yoreh Deah 268:12), Rambam in Hilchos Avodat Kochvim- and in the modern era in rulings by both HaRav Moshe Feinstein zs"l in Iggeros Moshe and the Satmar Rebbe (unsure of the exct reference for this last one).

Being ignorant of Judaism, the "messianic jews" try to counter this by taking a comment in the Talmud masechta Sanhedrin out of context- in reference to a passage in Yirmiyahu (Jeremiah)- the sages state that even when Israel sins, it remains Israel and does not loose its covenant with G-d. Sadly, their simplistic understanding of the text, and ignoring context and the rest of the law on this matter, leads them into a serious error here. How so? Yes- they remain Jewish- and if they do not repent they are PUNISHED, just as Israel was punished with the destruction of the Temple since they failed to repent! In other words this remaining Jewish is a two edged sword- on the one hand, if they repent they can return to Judaism (how easy we should make that return is debated and subject to differing rulings by various authorities), bu if they do not repent, then, as per the Mishnah in masechta Sanhedrin and Avos, they are punished with the most servere punishment possible! It doesn't matter that a non-Jew in the same religion doing exactly the same thing as them might be considered righteous, the Jew is judged and punished as a Jew, not as a non-Jew!

I consider myself Jewish, even though I'm in no way religious. My dad's whole side of the family is religiously and racially Jewish. I don't see my dad or his family is often as I want to, so I've never been much into the Jewish religion. But I do participate in the Jewish holidays.

Being Jewish is not just a religious thing, but a racial thing as well.

Hope I helped.