Now that opens up another whole can of worms.....
Yes, it is the SAME, and only, God, but, the Jews were the FIRST as a nation to worship the one, true God, who's personal name revealed to Moses as the "I AM". They do not nationally recognize Jesus as the Messiah, Son of God, or the triune nature of God, though their Shema (a prayer that is the centerpiece of the Jewish morning and evening prayers) encapsulates the monotheistic essence of Judaism: "Hear, O Israel: the LORD our God, the LORD is one", found in Deuteronomy 6:4, sometime alternately translated as "The LORD is our God, the LORD alone." Observant Jews consider the Shema to be the most important part of the prayer service in Judaism, and its twice-daily recitation as a mitzvah (religious commandment). It is traditional for Jews to say the Shema as their last words, and for parents to teach their children to say it before they go to sleep at night. (http://en.wikipedia.org/wiki/Shema_Yisrael). Interestingly, the last word echad means the unified and cardinal number one. Taken with the Genesis account where God said, "Let us create man in our image", alludes to a plural, but unified one.
So, even though they have not as a nation accepted Jesus as their Messiah, it nonetheless IS the same God (since He is the ONLY true God) that both Jews and Christians worship. The Muslims, on the other hand, worship a demon masquerading as the true god. Even a cursory read of the Koran would demonstrate that.
The Trinity is presented in the OT.
Besides, I don’t recall anywhere in the NT where having your theological ducks lined up was a requirement for salvation.