Perhaps you will find that the same session will admit one set of parents, and deny another. The reasons for accepting the one, and denying the other, could include assessing the "teachability" of those who desire to unite with the congregation, or who profess to be leaning toward the view that children of believers should be baptized.
Claiming submission to the church's teaching is a parameter not always easy to judge. We can probably come up with situations where potential members were eager to agree with a congregation's commitments, much like a fiancee could be willing to profess love-no-matter-what more on the basis of infatuation than dispassionate analysis. The members are absorbed, only after attending a carefully presented series of classes; yet, after a period of time a clash emerges based on unforeseen intransigence. The subject could be anything, while infant baptism might be no big deal.
My point is: sessions should be evaluating potential members only in part based on particular commitments in both doctrine and practice. Yes, any new Christian should understand that his submission to the sacrament of baptism and his subsequent participation in the Lord's Supper are not "optional." However, we don't ordinarily demand of new members that they precisely and concisely articulate the 5-Points, or be unwaveringly sold on Presbyterian polity, etc. We familiarize potential members with our distinctives, while trying to ascertain if these present a "credible profession of faith." Beyond that, we ask them to be teachable.
Most strongly convinced Baptist parents will not be good candidates (in my opinion) for membership in a specific Presbyterian congregation. Once they have heard-out the stance of the church they have contemplated, they may doubt for their own part the wisdom of committing to membership. Many people, however, are at the beginning (or somewhere along the way) of a path to a new desire for an increase in their faith, their religious understanding, their growth in grace. Are the people asking about membership in this local Presbyterian congregation, who may be Baptist-by-default, the kind of people who will submit themselves to the authority of the Word of God as it is taught and proclaimed by this church? That is what the session should be desirous to know.
Preventing otherwise submissive and teachable, responsible Christian adults-and-parents from finding their home among the saints in a dedicated Presbyterian or Reformed congregation seems unwise, unhelpful, unloving. In some ways, it seems like a preemptive judgment, an exercise of church-discipline in advance of evidence of intransigence and troublemaking. I do not think a hasty admission or one driven by pragmatic interest is a good one either. But it does seem to me there is a big difference between admitting to membership people open to learning and growing in Christ, and admitting those with a desire for the benefits of church membership only on terms that do not challenge a cherished alternative commitment.
