Thank you for your questions.
1. The OPC as a Church is committed to the Westminster Confession of Faith as a subordinate standard under the supreme authority of the Bible as God's word. It affirms, "The whole counsel of God concerning all things necessary for his own glory, man's salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture..." (chapter 1, section 6, italics added). The highlighted language expresses an important principle that bears directly on your second question. The teaching of the Bible, what the Bible may require, is not only its explicit statements but also what follows from those statements (of course always taken in context) by sound deduction. The biblical basis for baptizing infants, for instance, rests on this principle. So, the fact that the vows asked of parents at the baptism of an infant are not explicit in Scripture does not mean that they are unbiblical or should not be required.
2. The OPC's Directory for Public Worship orders our Church's worship, in conformity with the biblical elements of worship, according to the general principle, "all things should be done decently and in order" (1 Cor. 14:40). The four vows asked of parents at the baptism of an infant (the congregation may be exhorted but does not take a vow) facilitate good order in the Church for its well being. The substance of these vows elicits from these specific parents for this specific infant commitments that are biblical and essential for realizing the purpose of the sacrament of baptism.
3. The vows for public profession of faith/becoming a communicant member (by the way, these five vows, like the four made at the baptism of infants, are also not explicit in the Bible) do not have in view the commitment made by parents at the baptism of an infant. The membership vows are often taken by those who are not (yet) married and may never marry and have children or do not intend to marry. Further, those who are not (yet) convinced of infant baptism and may remain unconvinced may become members in the OPC (though by their membership vows they agree to receive our Church's teaching on infant baptism and, by implication, not to oppose it openly).
For these reasons there is biblical warrant for the vows made by parents at the baptism of infants.
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