I am going to answer all three of your questions in order. Most of this will be repetitious, but until it is understood, may be worth repeating.
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BTW, I still don't understand why erroneously baptizing unbelievers is an argument against credobaptism.
It isn't! I covered this earlier when I said that it is an argument against two things that some, but not all, baptists uphold. 1) Believers baptism. The London confession agrees with me in that
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Those who do actually profess repentance toward God, faith in, and obedience to, our Lord Jesus Christ, are the only proper subjects of this ordinance.
. 2) Baptism only for the elect, or those in the covenant of grace. Impossible to properly know who these are so we baptize all within the visible covenant.
Now, for the sake of making sure it is said again for clarity, we agree that adults should make a profession. We disagree as to the administration of baptism for children and their place within the covenant people(visible covenant).
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Does accepting non-believers into full membership of the church mean we shouldn't have church membership?
No. Different circumstance. However, could you show this link from scripture? As with the sentence below you keep equivocating baptism with the Lords supper. I have repeatedly asked you, and others, to show from scripture that they are the same and that the requirements for administration are the same. Baptism has rightly been administered to professorsand their OIKOS, whereas we have specific instructions concerning the table that are a bit different.
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Does it mean that, if a false professor should partake of the Lord's Supper, we shouldn't fence the table at all?