I need this cleared up once and for all.
Can one be called a Jew and a Christian at the same time ?
No.
You start being a Jew when you’re born one or when you convert, and you stop being a Jew when you worship another people’s god. That’s all there is to it.
That’s not all there is to it. Some folks disagree:
Huh? I’m pretty sure the Judeo and Christian God are one and the same. The main difference is that Christians believe that Jesus Christ is the son of God. Jews do not. I don’t see how you can be Christian and Jewish at the same time. To accept Christ as the son of God completely contradicts the basic tenets of Judaism.
ETA: I guess you can be considered of Jewish heritage, though, but a non-practicing Jew who believes Christ is the son of God is still a Christian, not a Jew from the religious belief standpoint.
Well, it appears that a Jew who believes in Christ may now operate a kosher establishment in Israel, so we must be getting pretty damn close to fusion:
Also, from Wikipedia, on Messianic Jews:
Although some Messianic Jews are ethnically Jewish, and argue that Messianic Judaism is a sect of Judaism,[9] the various streams of Judaism are unanimous in their rejection of Messianism as a form of Judaism,[10][11] and both Christians and Jews consider Messianic Judaism to be a form of Christianity.[12] Messianic belief in the divinity of Jesus is seen by the great majority of Christians and by Judaism as being the defining distinction between Christianity and Judaism.[10][12][13] This is also the opinion of the Supreme Court of Israel which ruled that the Law of Return should treat ethnically Jewish individuals who convert to Messianic Judaism same way it treats Jews who convert to Christianity.[14]
There’s Jews as Judaists and Jews as a people. I don’t have a problem with it. A Judaist cannot be a Christian, but a Jewish person can.
LHOD gets it. You can read much the same in The Jewish Virtual Library.
Per Orthodox rules you cannot run away from you Jewishness. You may be an apostate. You may practice Christianity. You may not even know that you are Jewish. But if you were born of a Jewish mother you are a Jew.
The Reform movement has a different take. Either parent can be Jewish but you must be raised with a Jewish identity to be considered Jewish.
Both accept conversions of course but the Orthodox won’t accept Reform conversions as, well, kosher.
You can be a Jew who has chosen to take on Christian beliefs but those beliefs are not Jewish in any way. The belief in Christ as a Messiah is a Christian belief.
Generally speaking, the answer the vast majority of Jews themselves give is “no”. If you deliberately adopt a different religion, you cease to be “Jewish” and become “one of Jewish ancestry”. Since Judaism has very little emphasis on “belief” as a part of faith, one can believe anything (or nothing) and still be “Jewish”, but identifying yourself as belonging to another faith is another matter. Hence a atheist or someone who believes in the Four Noble Truths (but has not “converted to Buddhism”) may be “Jewish” but a Christian cannot be.
However, Judaism isn’t the sort of religion, like Catholicism, which has a central authority capable of laying down the law - so there are always going to be different opinions on the matter.
Why this is relevant, is that there are some Christian groups who like to use whatever ambiguity exists to press for their own agenda - namely, to convert Jews to Christianity. These groups well understand that many of their targets will be more comfortable converting if they can take comfort in the belief that they are still “Jewish”. These groups really seek to use the internal controversies and lack of cohesion amounf Jews as a way, in effect, to destroy Judaism via conversion.
It’s a sort of Jew-jitsu. 
Most real, actual Jews are not fooled - this is mostly an issue that appeals to non-Jews.
Let’s end the silly semantics debate about what “Jew” mean by saying:
You cannot simultaneously believe in the Jewish faith and worship the Jewish God and believe in the Christian faith and worship the Christian God.
The Jewish God is one, indivisible–the most sacred, most central to everything Jewish prayer goes “…the Lord our God, the Lord is One (God)”–it’s a…the key concept–the central point of our belief in the Creator that He cannot be more than one being–he can’t simultaneously be God and Jesus and the Holy Spirit from a Jewish point of view. The Christian God is a Trinity. These are incompatible.
In addition, the Jewish lower-case-“m” messiah is a teacher and a king and not divine at all. The Christian capital-“M” Messiah is the Divine Son of God.
I’m not saying one is right and one is wrong, I’m not denigrating Christian or Jewish beliefs. But they are incompatible.
Just to make sure this is clear - from an Orthodox POV Jews who do not practice, especially Jews who take on another belief may be Jewish, but they are apostates, and that’s bad, very bad. Being a gentile is fine, you can be a very righteous person in their eyes by just following the seven Noachite Laws, but a Jew who rejects the faith … oh boy.
And “Jews for Jesus” would be considered as having rejected Jewish beliefs even by the Reform Movement. The staying legally Jewish while taking on beliefs that are incompatible with the most liberal forms of Judaism is no “comfort” to any Jew.
Sure you can, and it doesn’t matter if the beliefs are contradictory because this isn’t mathematics or indeed anything of any objectivity. I figure the beliefs are sufficiently arbitrary that any motivated individual can mash them up as he see fit, and if there are contradictions, that individual can simply choose not to think about them.
The issue isn’t whether one can think contradictory thoughts, but rather whether one can get others to accept that you have a contradictory identity.
Even given that, however, there’s a very reasonable school of thought to the effect that Christianity is a branch of Judaism. Its descendant, as it were. Christian religion is basically Judaism at the core, just with whast we believe are additional revealed truths which modified our previous understanding. To us, modern-day Jews are the ones who split off from the root.
Even though the two religions have a common ancestry, they are clearly different religions now.
After all, Islam believes exactly the same thing vis. Christianity - that Jesus was a legitimate prophet, that Islam is the “core” and that modern day Christianity is the abberation. Do Christians accept that they are, as it were, nothing more than incomplete Muslims? That a person converting to Islam can still be a “Christian”?
Particularly if the only ones interested in this possibility were Muslim groups dedicated to converting all Christians to Islam?
I think “others” will accept things that are arbitrary just fine. Heck, how much acceptance does one need? Government recognition? One’s entire extended family? A positive mention in the local media? The fellow members of one’s doomsday cult? For that matter, is it required to care about anyone’s acceptance?
How about Jesus?
That’s the nub of the matter - the majority of those who “care” do so because they want to make converts among the targeted community. They “care” about what these people think because they want to prostheletize and believe that acceptance will aid in that.
He hasn’t weighed in on the matter for quite some time. All we have are a lot of people who claim to know how to get the big J’s approval.
So what were the 12 Disciples?