"If you found out that there was no resurrection and that as we both think, that Muhammad was nothing but a nutter and a liar, we'll throw out Islam as worthless, but that Moses and the burning bush was for real, would you then follow all Jewish laws and rites? Judaism really all that different from Christianity. So what would you jettison ( Christian tenets ) from following, that you adhere to now?"
Yes.
I would need to actually see, not the burning bush, and not the flowing of the tide over the Egyptians (although I would want to see those things), but particularly God speaking on the mount to the assembled Jews in the loud and booming voice. Give me my time machine cum-cloaking-device-cum-universal-translator and let me see it happen, but then see that Jesus and Mohammed were frauds, and I would become a devout Jew.
You ask what tenets, and what would be different.
What KIND of Jew would be difficult for me, because the Temple is down and there are no Jews practicing the Judaism of the Temple. Orthodox and Conservatives practice the Judaism of the Talmud, which, of course, was written down after the destruction of the high priesthood.
There being no high priest anymore, and no Temple rites, it is difficult to know precisely what parts of rabbinnical Judaism are purely correct. My judgment is that Orthodox Judaism, but not the black-hatted Hasidim kind (whom I take to be culturally trapped in the stetl and preserving the culture of Ashkenaz but not perforce of David) is the closest. It would make aliyah and reside in Jerusalem, where I would spend the rest of my life in rabbinnical training and seek to become a rabbi.
I would follow all of the dietary rules, and all 613 commandments to the extent I could.
This is not a very hard question, really, for if one is certain of the existence of God, then the moral laws are fixed and it is only a matter of good sense to obey them and please the master. Really it is no different than good investment practice. Once you know you have a good, solid investment, you put your money there and earn the returns.
However, absent substantial proof of the religion, I am certainly not going to even pretend the adopt the dietary practices, nor keep the Sabbath, nor have my sons circumcised, none of that. I currently consider all of those things to be cultural practices parallel to the Greek rites concerning Zeus and Pallas Athena. I don't think God ever stood on a mountain and told anybody not to eat pork.
If I had proof he did, I'd forego my bacon and become a Jew.
Without that proof, I will not be a Jew.
The Hasidic movement began in Poland ( those hats are copies of 17/18th century hats worn by the Polish aristocracy ) and though I am no expert on the Hasidim, I don't think that they are close to what Judaism was when it began, nor even what it was 1,000 years ago.