According to the Baptist Faith and Message (2000- though it is also consistent with the 1925 and 1963 versions) a prerequisite for participation in the Lord's Supper is baptism by immersion. The Baptist Faith and Message 2000 (BFM) says the following in Section VII:
VII. Baptism and the Lord's Supper
Christian baptism is the immersion of a believer in water in the name of the Father, the Son, and the Holy Spirit. It is an act of obedience symbolizing the believer's faith in a crucified, buried, and risen Saviour, the believer's death to sin, the burial of the old life, and the resurrection to walk in newness of life in Christ Jesus. It is a testimony to his faith in the final resurrection of the dead. Being a church ordinance, it is prerequisite to the privileges of church membership and to the Lord's Supper.
The Lord's Supper is a symbolic act of obedience whereby members of the church, through partaking of the bread and the fruit of the vine, memorialize the death of the Redeemer and anticipate His second coming.
Matthew 3:13-17; 26:26-30; 28:19-20; Mark 1:9-11; 14:22-26; Luke 3:21-22; 22:19-20; John 3:23; Acts 2:41-42; 8:35-39; 16:30-33; 20:7; Romans 6:3-5; 1 Corinthians 10:16,21; 11:23-29; Colossians 2:12.
The New Hampshire Confession of 1833 is similar to the BFM, but the 1689 London Baptist Confession does not state such a requirement.
I had an exchange with someone named Steve who was antagonistic and basically called my ability to be a Southern Baptist into question because I said- and I stand by this statement- that I do not agree that a believer that was baptized by a method I disagree with should be excluded from the Lord's Supper. I see this as something for believers in Christ, Christians, with even baptism- though vitally important- being a side issue. I feel that as the 1689 London Baptist Confession states (in 30.1), the Lord's Supper is "to be a bond and pledge of their communion with Him [Jesus] and with their fellow believers." I believe that God has directed us to live in unity as Christians and that the Lord's Supper should promote that idea, not detract from it.
Behold, how good and pleasant it is
when brothers dwell in unity! (Psalm 133.1 ESV)