You forget that the Hebrews were "Babylonians" or Semites.  When they went into captivity in Egypt the Babylonian-Canaanite--Egyptian--Greek-Hebrew religion was a continuum. So the Babylonian DNA never ceased.

Because of musical idolatry at Mount Sinai God turned them over to worship the starry host and sentenced them to return to Babylon:

Acts 7:43 Yea, ye took up the tabernacle of Moloch, and the star of your god Remphan, figures which ye made to worship them: and I will carry you away beyond Babylon.

It was the Babylonian Captivity which largely cured the Jews of idolatry so that with a minor exception the Temple was abandoned and the sacrificial system ended. The spiritual people continued with the Synagogue which began in the wilderness.

It is a fact that the operatives at the time of Christ were hirelings and most of the rituals of the time originated in Babylon. These were demolished by real or acted parables by Jesus.

The passover was a Babylonian festival and Jesus instituted the Lord's Supper in the midst of unleavened bread.  However, most babyonish churches perform the memorial as the Babylonian passover.

The cross or staurus and the words connected with baptism seem to me to be directed to COOLING the passions and pride of the people which led to imposed blood rituals when God turned them over to a national (goyim) king. Animal sacrifices are not to be seen as COMMANDED but IMPOSED because the people refused to walk by the original covenant which included no mandatory sacrifices and no priestly clergy.

In Galatians 5 when Paul warned about crucifying Christ all over to ourselves the word is exactly the opposite which means religious rituals which STIR UP THE PASSIONS and pride which come from the flesh and not the spirit.

Sounds like an interesting read.