Sure. There are Jews who are actually racially Semitic, i.e. genetically related to the Hebrews, and all other Semitic peoples. But, according to the Jewish law, you are a Jew if your mother is Jewish. The genes don't matter, be they father's or mother's! It's the mother's "Jewishness" that matters.
The mother, for all you know, could be a convert to Judaism who could be genetically completely unrelated to anything Semitic. The "Jewishness" of the mother (whatever the criteria) is somehow indelibly "imparted" to her children so they are all born "Jewish."
Is being "Jewish" an ethnic or religious or national issue? I guess, it depends what suits you (or what will give you a visa out of the country you don't want t live in).
According to the Society of Humanistic Judaism" [all emphasis are mine] "There is no single way to be Jewish..." [surprise!]. The Society affirms that "Secular Humanistic Jews encourage and support activities that promote the continued development of Jewish identity." (which by their own admission is an elusive concept). However, it all basically boils down to "a deep attachment to the state of Israel, its culture, and its people."
Furthermore, the source states "Secular Humanistic Jews make no distinction of any kind among Jews who, regardless of parentage, have chosen to identify with the Jewish people."
Yet being a Muslim or a Christian prevents you from being considered Jewish in Israel or by the Jewish Community at large. The Israeli Law of Return is a law that grants immigration rights only to the Jews without a prior naturalization process; that is – to those individuals who "fit" the official (rabbinical) definition of "Jewishness." The Law simply states that "any Jew may come to Israel and become a citizen without undergoing naturalization."
Specifically, zionism-israel.com's Ami Isseroff explains that "Israel's immigration policy is not racist or separatist. In common with many other countries, it gives precedence to its own absent nationals."
So, Israel treats Jewishness as an inherent nationality (that is a matter of choice), independent of where you were born or how many generations have passed. Others treat it as a religious affiliation, and others yet as a racial/ethnic quality. [covering all the bases, I guess...]
As for Messianic Jews, they are a periphery, embraced only by such Christian groups as the Presbyterian Church [sic] (U.S.A.) which for a long time was in "communion" with Avodat Yisrael. Messianic "Jews" are Protestants in disguise with Jewish terminology and Jewish-sounding names. Their aim, of course is to "save" as many Jews by converting them to Jeezuhs.
Jasom Baysee, a pastor of Shady Grove United Methodist Church in Providence, North Carolina, writes in The Christian Century "If there is anything about which all four branches of Judaism in the U.S. (Orthodox, Conservative, Reform and Reconstructionist) agree, it is that one cannot be both Jewish and Christian at the same time."
If you are going to be a religious (observant) Jew, you cannot worship any other God except the YHWH of the Old Testament. The Jewish messiah is not a divine person. That automatically disqualifies Jesus as a possible Jewish messiah. The idea that the messiah is a divine person is a Christian innovation that was rejected, along with all Christian books, by the rabbis in Jamnia at the end of the first century AD.
Messianic (Apocalyptic) Jews of the 2nd century BC (Pharisees and Essenes) expected a messiah to be a mortal warrior-king (there are 7 OT determined requirements for a messiah and Jesus meets only one, being Jewish). As such a messiah for the Jews is not an incarnate God-man who, together with the Father and the Spirit is worshipped and glorified. That is heresy in Judaism across all sects.
So, they cannot deny that someone "born" Jewish is Jewish by Law, but if they worship any other deity (and no, the Jews do not think Christians and Muslims worship the same God as the Jews, because then they would have to admit that Christ is God and Allah is God, which they won't!), they are no longer Jewish, but apostates no different than all the other Jews who worshipped false gods in the past.
Not sure where you get all your proof texts from, but the few you mentioned cannot be considered all the info there is on the subject. I prefer to take people at their own word and not how some others would define them. One of my professors, Dr. Mark Cambron (now deceased), had a specific Christian ministry to the Jews in Miami, FL. You can do a search about it and he was and is not alone, by far.
As to worshipping YAHWEH/Jehovah, he IS the only true God and Jesus Christ is God in the flesh. Isaiah 7:14, 9:6 both prophesy that the Messiah would be the Incarnate God. There are other OT verses as well, as you know, so to say the early Hebrews did not believe in a divine Messiah is simply not correct. And there are hundreds of Messianic prophesies, not just seven. Now the Muslim god, Allah, is NOT the same as YAHWEH. Not even close. To simply say it is just the Arabic word for god is to ignore the description of Allah given by Mohammed. No comparision at all. There is a reason the term Judeo/Christian is used in this country as it recognizes the worship of the one true God.
We sure are hopping all over the theology subject in this post, aren’t we?