On Baptism and Memborship

Something that is always seemed ironic to me is the general theology of Baptists regarding baptism.

On the one hand, they will argue to death with their Lutheran friends that Baptism does not save, regenerate, remove original sin, etc, and is basically a symbol, or profession of faith to the outside world and the local church body.

On the other hand they are the most paticular about HOW it should be done, namely, by immersion, otherwise it is not a real baptism, and they must be baptized again.

Doesn't this seem backwords. If you believed it was somehow changing something I would think you would be much more paticular about the form, method, exact wording, less you messed it up and didn't affect regeneration, etc. Why would you NOT be making a public profession if say only 80% of you went underwater or whatever. Would the local body gets confused about whether you truly professed, only to see that, indeed, you did truly when you were rebatized to make it right?

It seems this is rather important, especially surrounded memborship. I guess all Baptist churches wish only a regenerate body, so some sort of memborship makes sense (indeed, because you allow non-christians to come to your services), but what else does memborship entail. If a believer is attending your church but does not have memborship how are they functionally different. One that I can think of is perhaps if you are congregational and everyone votes for things, you would only want membors to vote, namely those who are committed and feel they are part of the church, etc.

But anyway, if someone was a believer in a methodist church (and there are a least a few that I know of ) and was baptized there (as an adult), how is it that is not an adequate profession of faith. Is there something else to baptism that makes this inadadequte?

Perhaps the best way to ask this queston is, what is baptism?