We are back once again to the difference between how reformed Presbyterians and Reformed Baptists tend to see this issue.Lighfoot cites Maimonides:
II. All the nation of Israel do assert, as it were with one mouth, that all the nation of Israel were brought into the covenant, among other things, by baptism. “Israel (saith Maimonides, the great interpreter of the Jewish law) was admitted into the covenant by three things,—namely, by circumcision, baptism, and sacrifice. Circumcision was in Egypt; as it is said, ‘None uncircumcised shall eat of the passover.’ Baptism was in the wilderness before the giving of the law; as it is said, ‘Thou shalt sanctify them to-day and to-morrow, and let them wash their garments.’ ”
III. They assert, that that infinite number of proselytes in the day of David and Solomon were admitted by baptism: “Thex Sanhedrims received not proselytes in the days of David and Solomon: not in the days of David, lest they should betake themselves to proselytism out of a fear of the kingdom of Israel: not in the days of Solomon, lest they might do the same by reason of the glory of the kingdom. And yet abundance of proselytes were made in the days of David and Solomon before private men; and the great Sanhedrim was full of care about this business: for they would not cast them out of the church, because they were baptized,” &c.
IV. “Whensoever any heathen will betake himself, and be joined to the covenant of Israel, and place himself under the wings of the divine Majesty, and take the yoke of the law upon him, voluntary circumcision, baptism, and oblation, are required: but if it be a woman, baptism and oblation.”
John Lightfoot, A Commentary on the New Testament from the Talmud and Hebraica, Matthew-1 Corinthians, Matthew-Mark, vol. 2 (Bellingham, WA: Logos Bible Software, 2010), 55.
One can see that washings were the norm; it is the particular washing that is important in John's case-a shift had occurred.
Consider the gospel that Abraham rec'd, the apostles and Christ preached and the gospel of our age. All, very different in application, but yet, the same in essence.