Alien baptism means an unbiblical or defective baptism such as infant baptism, or someone baptized in a baptismal regeneration church, or a false profession baptism. We would not hold to alien baptism as practiced by Landmark Baptists who refuse to accept any baptism except those performed under the auspices of a Landmark Baptist church.
When Christ gave the Great Commission in Matthew 28:19-20 he commanded the church to make disciples by winning sinners to Christ and then baptizing them. So if a person makes a false profession and is baptized by immersion in a Scriptural local church by definition that baptism would not be a Biblical baptism and therefore an alien (or at least an unscriptural) baptism. That false professor would need to be saved and baptized as a believer.
A Biblical example sometimes cited by those who espouse this position is the rebaptism of John’s disciples in Acts 19:1-7. Paul asked the twelve, “Unto what then were ye baptized? And they said, ‘Unto John’s baptism.’ Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus. When they heard this, they were baptized in the name of the Lord Jesus.”
We as local Baptist congregations should not allow persons to join our churches who have not first of all trusted Jesus Christ as their Savior and been Scripturally baptized by immersion. If they had been saved and baptized by sprinkling or pouring or in a church, such as the Church of Christ that believes in baptismal regeneration, then that person should be baptized by immersion understanding the significance of baptism as a picture of the death, burial, and resurrection of Christ.