Jesus is a New Testament figure and very explicitly broke with the past in key ways. This is why his followers are not required to keep kosher, commit genocide, or abstain from having tattoos or mixed fiber clothing.
No, they're not required to keep kosher, commit genocide, or abstain from having tattoos or mixed fiber clothing because he fulfilled the law, not because he replaced it[1].
Furthermore Jesus was the God of the Old Testament, at least if you accept the New Testament as scripture[2].
[1]: "Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil." --Matthew 5:17
Your first paragraph is repeating my point: Christians are not bound by the same rules as the Jews in the Old Testament.
As for the second, you’re leaving out the last couple of millennia of Christians debating the exact nature of God and fissuring into different groups over the details. Most variants recognize some difference between the OT and NT gods, however, because you have to explain the difference in their actions and instructions.
