“If the purpose of water baptism was to make the Jews a kingdom of priests (Ex. 19:6), did women have to be baptized?”
It’s true that Jewish men were baptized because priests had to be baptized (Ex. 29:4), and only men could be priests. But water baptism was also “for the remission of sins” (Mark 1:4; Acts 2:38), so women needed to be baptized under God’s kingdom program for Israel for that reason. That’s why we read,
“But when they believed Philip preaching the things concerning the kingdom of God… they were baptized, both men and women” (Acts 8:12).
Don’t forget, when the Bible says things like, “God… will have all men to be saved, and to come unto the knowledge of the truth” (1 Tim. 2:4), the Greek word for “men” there is anthropos, from which we get our word anthropology, the study of mankind, both men and women. Be sure to keep that in mind when you read Paul say to “live peaceably with all men” (Rom. 12:18), “do good unto all men” (Gal. 6:10), “abound in love…toward all men” (1 Thes. 3:12), “be patient toward all men” (1 Thes. 5:14), and “make all men see what is the fellowship of the mystery” (Eph. 3:9). source