Modern day Judaism is one of the religions I probably have the least amount of time studying it.
There is a ultimatum in Christianity. In which Non-believers will be in hell for all of eternity regardless of their good works they all fall short and did not believe in the true living God.
Does Modern day Judaism have a ultimatum?
For example if Modern day Judaism were true what would happen to Christians?
Judaism, especially modern Judaism, doesn't have the same kind of expectation for theological cohesion that Christianity does. One way I've heard it put is that Christianity is an orthodox religion (right belief is what is important) whereas Judaism is an orthopraxic religion (right practice is what is most important). As such, Judaism focuses far more on practice, observing Torah, with major Jewish religious commentaries and works of religion focusing on practice and interpreting Torah as a matter of practice (e.g. the Talmud, Jewish halakah, etc). Whereas in Christianity we have focused more, in our religious commentaries and how to interpret Scripture about what we believe and confess (the writings of the fathers, the Creeds, the various confessional statements, catechisms, etc).
What this means in this context is that there isn't a unifying Jewish belief about the afterlife. Rather there are numerous ideas and opinions that have been put forward down through the ages by various rabbinical authorities which do not agree with one another. Jewish commentaries, for example the Talmud, present competing opinions and provoke more questions, "Rabbi So-and-So said this" "But Rabbi Such-and-Such said this" and so what an individual Jew believes about certain things is a matter of personal opinion rather than religious obligation. There are, of course, unifying Jewish beliefs, but they tend to be focused around a small list of "essentially Jewish" ideas. For example, there is only one God, because the Torah says to worship no other god but YHWH.
The closest thing Judaism has to a "creed" would be the Thirteen Principles of Faith by the medieval Jewish sage Maimonides. Which affirms the oneness and unity of God as the only God and Creator, in the divine inspiration and giving of the Torah, a belief in judgment and reward, the coming of the Messiah, and resurrection of the dead. The Thirteen Principles can be found
here.
Note that a belief in judgment/retribution and reward, and a belief in resurrection affirms a belief in life-after-death. But what all of that means exactly is still up for debate and open to opinion. Jewish sages throughout the centuries have said that time spent in hell, for most, is only partial, a kind of purgatory where the wicked are punished and cleansed of their sins before finally being able to enjoy peace in death. Other Jewish commentators have argued that the most wicked will spend eternity in hell. Some Jews don't believe in a literal hell at all. Other Jews believe in reincarnation, where an individual soul will go through several lives until finally attaining resurrection when the Messiah comes.
In Judaism being Jewish is not a requirement for experiencing the Olam Ha-ba (World to Come or Age to Come), but that when the Messiah comes both Israel and the righteous gentiles shall come together. Based on, for example, the words of the Hebrew Prophets who speak of the nations coming to Mt. Zion and joining with Israel in the future messianic age.
In Judaism, generally speaking, if there is a hell it is viewed as a time of purging and purification for the soul, but could mean an eternal punishment for the most wicked. Basically, your average sinner might spend a year in hell, but someone like Hamaan from the Book of Esther would suffer forever because of the depths and severity of their misdeeds. But, again, there's no unifying belief about hell in Judaism, or even if there is a hell at all.
To add even more complexity to this, opinions and views change even more depending on which branch of Judaism one comes from. An Orthodox Jew and a Reform Jew will have very different ideas about a lot of things. And then a Hasidic Jew even more different. And that's just speaking of normative Rabbinical Judaism. While Rabbinical Judaism is what "Judaism" almost universally always means, as this is the Judaism that descended from the Pharisees (basically the only major surviving sect of Judaism to survive the destruction of the Jewish Temple in 70 AD). There are also Karaite Jews, a relatively small and independent Jewish sect whose origins are still debated, Karaite Jews are notably different from Rabbinic Jews in that Karaites reject the Oral Torah (Mishnah), and thus do not consider the Talmud a valid authority; they are sometimes called Tanakh-only (Tanakh being the Jewish Bible, roughly being the same as the Protestant Old Testament) Jews as they only accept the Jewish Bible as their source, and thus their opinions on halakah (Jewish observance) depends only on the text of the Torah.
An example of the differences between Rabbinic and Karaite Jews is that Rabbinical Jews understand the commandment to not boil a juvenile goat in its mothers milk as a general prohibition against mixing meat and dairy together. Karaite Jews, on the other hand, take a more narrow and strict interpretation, and that it does not prohibit mixing meat and dairy generally, but prohibits, well, taking a goat's meat and boiling it in the milk of its mother.
This probably doesn't provide a clear answer to any of the questions posed, but should help provide at least some general ideas and invite further research. I've personally been fascinated by Judaism for many years, and have found benefit in speaking with practicing and observant Jews. Both because I enjoy reading about other religions, and also because Judaism has a special place within the history of Christianity. I've frequently found that Jewish insights have helped me in my own understanding of biblical history and thus frequently provides a helpful insight into the time and context of the New Testament and early Christianity.
-CryptoLutheran
