Redemption of the firstborn was a Jewish tradition in the Old Testament that was given to the Jews to mark the events of the Passover night while they were in Egypt. This practice had strict obligations and exemptions. It was about redeeming the firstborn son of a family from the obligation of life-long priestly service and not about redeeming them from evil forces. The tribe of Levites were exempted from this ceremony because they were supposed to be in the service of God for life.
The firstborn performed the priestly function until the Israelites got to the wilderness, and then the priestly duties were assigned to the tribe of Levi. This duty was strictly expected of the firstborn son of a Jewish mother (a firstborn son by a non-Jewish mother was exempted); that son was to be bought back from God to their family, and thus exempted from this service. If a woman’s first child was not a male, or if the child was not of the first pregnancy (if a previous pregnancy ended with a female child, abortion, or miscarriage), the law was nullified for that family. There are many other details of this tradition including washings, festive meals, dressing requirements, manners of presentation, and other provisions, which the people who teach and practice firstborn redemption today do not abide by as prescribed in the law.
It was a one-time ceremony for these specific firstborn sons, and not a ritual that was repeated monthly, quarterly, or yearly as people currently practice it. The redemption amount was equal to five silver coins, nothing more, and nothing less (Exodus 13:2,12-16; Exodus 22:29; Exodus 34:20; Leviticus 12:2-4; Numbers 3:11-13,45-51; Numbers 8:17; Numbers 18:16). The law was an all-or-nothing system. If you adopt any of its ordinances, you must strictly abide by its provisions or else you fail in all. The sacrifice of Jesus was sufficient to buy eternal redemption for all. Redemption of the firstborn was a shadow of what Jesus would do, as the firstborn of new creation on the behalf of humanity (Romans 8:29; Colossians 1:15,18; Hebrews 12:23). The Old Covenant, its priesthood, and all its associated rituals have been abolished and changed (Ephesians 2:15; Colossians 2:14; Hebrews 7:12).
The redemption from Satan and the bondage of sin unto God that Jesus bought for us through His blood is full, complete, and to the uttermost. Furthermore, He has made us priests and kings unto God (1 Peter 2:9; Revelation 1:6; Revelation 5:10), so we cannot be redeemed from this priestly calling (as was the purpose of the redemption of the firstborn in the Old Testament).
Some may be doing this sincerely out of ignorance because that was what they were taught. However, some others have found it a money-making scheme, asking people to pay some amount of money to be redeemed. This is an insult on the blood of Jesus.
To perform redemption of firstborn as a believer today is to say that what Jesus did was not sufficient, and thus to negate the grace of God.