Mark Jones
Let me be the first (perhaps not) Baptist to admit that Mark Jones was spot on in many regards in his post “A Plea for Realism”:Are Presbyterians Christians? It seems to me that Mark Jones is simply calling for a little intellectual honesty from us Baptists. Well, allow me to humor him.
I certainly agree that, if we do not allow unbaptized believers to take communion, that should include those who have been “baptized” in a way that we believe to be unbiblical and, thus, no baptism at all. If a paedobaptist came to my church who refused to be baptized post-confession due to having been sprinkled as an infant, we would not allow him to be a member, so why would we allow him to take communion? Baptism, in every Christian tradition, has historically preceded communion. Baptism preceding communion is both a historical and a biblical view. On this point, most Baptists and Presbyterians agree.
Therefore, for me to dissuade my Presbyterian friends from taking communion in my local church, I am not saying they are not Christians so much as that they have not followed biblical mandate in regard to the order of the sacraments. That is, baptism precedes communion. On this point, they would obviously disagree with me, because they hold to a different understanding of baptism. However, for Baptists to cave on this issue and allow for unbaptized Presbyterians (and that’s what we think they are) to take communion, we would be going against our confession’s definition of true baptism.
However, we are not alone in this stance. Presbyterians must take issue with at least some Baptists taking communion in their churches. Just this week, I listened to a somewhat refreshing episode of Reformed Forum in which Jim Cassidy admitted that Baptist parents are in sin who do not baptize their infants in keeping with a Presbyterian view of baptism. I think this is the only consistent Presbyterian view and, as such, I don’t see how Baptist parents can take communion in Presbyterian churches, unless Presbyterians encourage people in open, unrepentant sin to take communion.
Either way, both traditions have an issue when it comes to what Jones calls “catholicity” and baptism. Neither one of us can deny that we see the other as being disobedient to our Lord’s ordinance of baptism. Are Baptists inconsistent to call their Presbyterian friends Christians? Not quite as inconsistent, I would argue, as those Presbyterian churches that allow consistently Baptist parents to take communion.
So, perhaps the proper way to respond to our Presbyterian friends when they try to corner us on these issues is not to bend over backward to try to be ecumenical. Perhaps, the best response is to affirm them where they are correct, but demonstrate how they have to answer the same questions regarding their sacramentology. None of us are immune. At a certain level, each believe the other (credos and paedos) is disobedient at a certain level, and that must stand as a guard to the communion table at some point.
See also Tom Hicks’ response to Jones’ article. Michael Haykin has also chimed in, and Jones has offered his critique of Haykins’ response here.
CredoCovenant 
I am not Presbyterian and not paedobaptist. I grew up in a church with closed communion (for denomination members only). However, I do not subscribe to communion for credo-baptized folks only. To do so makes baptism a first order belief (vital to salvation). I do not believe it is. Baptism is not the basis of life in Christ, it is a corollary. In my judgment only beliefs and practices which cast doubt on salvation and attack the heart of the gospel should sense from fellowship. If we can have informal fellowship we should be able to have formal fellowship ( if there is such a thing). I would wish to welcome all Christ has welcomed.
The question is not whether or not baptism is necessary for salvation. No one is arguing it is. The question is what purpose baptism plays in corporate life. Baptists, Presbyterians, Methodists, Anglicans, and Pentecostals, pretty much all Protestant churches and even Rome against whom they protest, all agree that one joins the church corporate through the rite of baptism. For Presbyterians, baptism is a corporate affirmation of the candidate’s having entered into covenant with God and with the covenant community. For Baptists, the same is also true, but we argue that only believers can receive the sign because only believers are in the covenant (hence, CredoCovenant). Communion is also a corporate act. It is an act in which all peoples in the covenant community who are in good standing with a local church and in good conscience participate. How is one initially affirmed by a local church as being in good standing? Baptism. Were Baptists not to dissuade unbaptized Presbyterians to take communion in Baptist churches, they would essentially be denying their own definition of baptism and their understanding of church membership.
Sprinkling or even dunking an unbeliever (as was first the practice with infants) is no baptism. That is the biblical (and Baptist) view of this command and ordnance. Within a Baptist church only those who have been obedient and are repentant believers are welcome to the Lord’s Table. This means no unbaptized Christians are to take communion at a Baptist church.