In What If He Can’t Be Baptized? Nathan Finn addresses the question, "What should we do if someone comes to faith in Christ and desires to be baptized and join our church, but she cannot be baptized due to some sort of medical condition?"
In this post Brother Finn notes four variations he has heard suggested by Baptists. Respondents in the comments section suggest two other possibilities, bringing the total to six.
1. "some Baptists argue that the individual should not be baptized and should not become a member of the church or receive the Lord’s Supper."
2. "some Baptists argue that you should immerse the person anyway"
3. "some Baptists argue that you should 'baptize' the person by sprinkling or pouring."
4. "some Baptists argue that you should not baptize the individual at all, but should allow her to become an unbaptized church member"
5. Shadow baptism (a waterless type that mimics the actions of immersion)
6. Proxy baptism (allowing another to be baptized for them)
First of all, if the immersion in water of a penitent believer is the biblical act of baptism, then no other act or substitution is biblical baptism.
Second, while certain "anti-Baptists" may exaggerate the difficulty, there are real-life exceptional circumstances. Most recognize death-bed situations and do not require baptism because the believer is incapable of either it or the church membership, Lord's table, continuing in the apostle's doctrine and other elements that would normally follow. In addition to the bedridden, certain medical conditions that might make immersion near impossible to impossible -- individuals who are quadriplegics, individuals with tracheotomies (an opening into the airway in the throat), individuals with an autoimmune deficiency/severe combined immunodeficiency disease that requires living inside of sterile cocoon chamber, or individuals in negative pressure ventilators (commonly called "iron lungs") or other mechanical ventilation. There is also the question, for some, about individuals whose medical condition is psychological rather than physical, for example exhibiting a severe phobia of water or immersion or both.* Individuals who have undergone recent medical procedures may be able to defer baptism until after their recovery.
Third, in some senses this a uniquely Baptist dilemma. Anyone placing salvation in the baptismal waters must go through with the rite of baptism or risk the eternal soul of the candidate (though the Mormon might perhaps allow a later proxy baptism). Those who see no significance in water baptism merely dismiss the dilemma -- for there is none. What's the big deal? Baptism doesn't matter.
Finally, I find a "Baptist answer" only in 1, 2, or 4. Suggestions No. 3 and No. 5 ignore the reality that immersion in water is baptism. You are actually practicing No. 4 even when you practice Nos. 3, 5 or 6. We can't immerse a person by sprinkling or pouring, or by some type of "Charades" ceremony. These reject the command, principle and example of biblical immersion baptism in favor of a counterfeit designed to make someone or some set of someones feel good. Folks have not been biblically baptized if they have not been immersed. Suggestion No. 6 has no biblical sanction and suffers many of the same problems of three and five.
The proponents of suggestion No. 2 either deny the reality that there are real cases in which there is actual danger, or simply do not care. Suggestion No. 1 is not technically wrong regarding baptism, but might be unnecessarily rigorous and legalistic to apply to persons who would obey if they were able, but are physically incapable of obeying. Yet those choosing this option might embrace the Christian in all other ways possible while withholding only any privileges for which they see baptism as prerequisite (i.e., church membership & Lord's Table). Years ago I read the conclusion offered in suggestion No. 4. I wish I could remember this source, but my memory is that this was suggested by some older Baptists who were conservative and offered it as only a last resort in very exceptional cases--When immersion is impossible the intention should be accepted for the act (with a possible reference to the thief on the cross). The stricter Baptist who adopts No. 4 is sure this option is only for exceptional cases, want to take care that these are indeed "exceptional" cases (not just someone making excuses, for example), and fear the precedent they may be setting. There is a legal adage that "hard cases make bad law." It's not difficult to understand how exceptions can begin to be applied across the board and churches start practicing the easy exception rather than the harder rule. To me it appears that the proponents of suggestions No. 1 and No. 4 intend to "err on the side of caution" -- but "err" in different directions. No. 4 errs toward the person, where No. 1 errs toward the act.
At this point (mentions of Spirit baptism notwithstanding) the only scripture that I have found or thought of that seems to have some application to this issue is the death of the converted thief on the cross. See Luke 23:32-43. Jesus did not use His power and authority (or 12 legions of angels) to stop the crucifixion in order to have the thief baptized. The thief's physical condition rendered the rite impossible. Jesus did not ask the disciples to throw water up on the thief, neither did He suggest that they observe a proxy baptism at a later date. The thief was forgiven by Jesus and "made acceptable in the beloved." Here we might imagine that any sincere intention that the thief had was accepted as the act. But since the thief was dying and not a candidate for church membership (or the Lord's Supper later), it doesn't shed much light on suggestions No. 1 and No. 4.
*These are medical conditions that have been suggested. For the sake of argument we will not worry over which ones might or might not be valid conditions rendering immersion impossible. But, for example, quadraplegics have been baptized, though with difficulty and much preparation. (Daily News, Bowling Green, KY, May 1, 2000, p. 3a)