All baptisms should be carried out by the authority and vote of a local church.
The membership attests to the testimony of the baptism candidate and with the act of baptism, one is received into the church. To the church and to the world, the one being baptized is testifying that their "Old Man" is dead, that they have been raised to walk in newness of life. Whatever their old identity, their new identity is with Christ and his Church.
Without the Church, there is no baptism.
If I go down to the lake or swimming pool, and dunk folks without local church authorization, there are few if any churches that would accept such baptisms, nor should they.
There are to be no "freestyle" baptisms outside the authority of a local church regardless of the "credentials" (or lack thereof) of the one who is performing the baptism.
If a church (properly organized and functioning) decides to have a baptism service at a lake or swimming pool and is performed otherwise in a biblical manner (trinitarian, upon their profession of faith, etc.), such a baptism should be without question.
My last church in Southern California performed its baptisms during "Life Group Fellowships" (small group meetings) where people were baptized in swimming pools, jacuzzis, etc. Such was under the oversight and direction of the Church elders. Not sure I would completely agree today but it is without question that such baptisms were performed under the authority of a local church and are therefore valid.
Some Baptists take the position that the administrator should be an ordained minister, but I don't see any such requirement in the Bible.
There are a few things we can say about this.
First of all, one could argue whether ordination is even scriptural? I believe that the "Recognizing, laying on of hands, and sending out" is demonstrated throughout the scriptures and this is where the practice of licensure and ordination is based so I believe this to be a good practice that should not be neglected or diminished.
We have Jesus's words that "Whatsoever you shall bind on earth shall be bound in heaven..." which I believe may be applied to certain practices within a local church that may differ from one to another. The scriptures do not mandate that an "ordained minister" be the one who does the dunking but if a Church congregation makes it their requirement, then one is bound to honor this and recognize the authority of the one to whom such is given.
With all of this said, it is understood that it is the local church that has the authority to baptize. It should also go without saying that the church has the RESPONSIBILITY to ensure that the baptism is properly administered according to a specified criteria. The Church is responsible to ensure that the task is delegated to someone who is adequately equipped to understand doctrine and exercise discernment in the counsel of those who desire to be baptized. Such a task is therefore usually delegated to an adequately trained pastor/elder.
In our church, it is common practice that the pastor performs all of the baptisms. Baptisms are performed once or twice a year and baptism candidates are required to attend classes that are taught exclusively by our pastor. During these classes, the pastor gets to know the candidates better and is able to assess the validity of their "conversion experience," evidence of regeneration, etc.
And with all of this being said, I would be perfectly fine with my pastor delegating the actual "dunking" to be performed by someone else so long as he continued with his diligent "screening" and "gate-keeping" of candidates. There are some churches that allow parents to baptize their own children (during a formal baptism service) and so forth. I have seen such being turned into a literal "Party" atmosphere and I do believe we need to maintain th dignity and solemnity of the occasion. I believe that the person performing the baptism should be someone who is a "spiritual leader" who will take ownership of this individual for discipleship and integration into the church body.
As I hinted in a previous post, it would be a wise policy for churches to accept baptisms only from other congregations that they recognize as a true church of "like faith and practice," however that is defined. If the applicant for membership was "baptized" in another "church" that is not recognized as a true church, and to which they would not be willing to dismiss members with a letter of good and regular standing, then it would be inconsistent to accept their baptism.
I believe this involves discernment that extends far beyond the actual baptism. What makes a church to be a "True Church" and what lines need to be drawn in order to distinguish a "true church" from a "false church?" We need to be careful in our definitions here delineating the essential core doctrines which define the historic, orthodox Christian faith. Far too often, we argue over matters of eschatology, ecclesiology, election/free will, cessationism/continuationism, and so forth. Do we really want to dismiss as a "False Church" a congregation officially holding to a "Pre-wrath" position over a "Pre-Tribulational Rapture?" There are some who do just this but would this be right? Should we not "call out" such as being overly contentious and divisive?
I would be very cautious regarding any baptism from a congregation having "Restorationist" roots (anti-creedal/anti-confessional). JWs, LDS, and SDA, are obvious. Cambellite Churches of Christ that teach "Baptismal Regeneration" should also be rejected. There are some "Disciples of Christ" and "Christian" Churches that are more orthodox but since they still do not hold to any "creed" or "statement of faith," it is often difficult to exercise proper discernment from one congregation to the next.
While I would never recommend any Pentecostal or Charismatic denomination, I would also acknowledge that the Assemblies of God (for example) has a very robust statement of faith and aside from their arminianism and continuation of "sign gifts," etc., they easily pass my orthodox "smell test" and for this, I would not dismiss them as being a "false church." If someone were coming from a more radical congregation such as "Word of Faith," Bethel or whatever, I would be significantly more hesitant and would never regard such as being a "true church" any more than I would consider the Roman Catholic Church as being a "true church!"
If, on the other hand, Arnold Caines (Calvary Chapel affilliated) were to come to my church, I would receive him without hesitation and possibly recommend him for a future leadership position!
There are many other "Rabbit Trails" we could go down and explore. As I have stated elsewhere, Paul Chappell (Lancaster Baptist) accepts only "Baptist Baptism" in the interest of "Doctrinal Purity" but I would argue that achieving doctrinal purity (which is important) is far more complicated than just ensuring that everyone is baptized with the "right baptism" right? What I would do is begin with a very robust SOF that outlines specifically what our congregation believes and teaches as well as reasonable standards of conduct of which we would expect of each member. Such would be covered in the church's constitutional bylaws and membership covenant. This would be reinforced with sound, expositional teaching and preaching where one would become better grounded in these doctrines and adequately equipped for whatever God's calling is for you in our local church body!