“Do Jews and Christians worship the same God?”
There is a sense in which we do, or at least could potentially. YHWH, who revealed himself to the Israelite patriarchs, who brought a slave nation out of Egypt with signs and wonders that astonished the nations, who gave Moses the law, who brought Israel into Canaan, who established the Davidic dynasty, who sent first Israel then Judah into exile among the nations, and who brought Judah and members of the other tribes back to Jerusalem — this is the same God Christians worship today. He has not changed.
Jewish beliefs have changed over the centuries since Christ died though, and here lies the real issue.