The 3FU are not as specific about the requirements for entrance to the Lord’s Table, and so there will not be quite as many places at which the PC advocate would have to take exception. However, there are still quite a few places.
HC Q. 75: the Lord’s Supper reminds and assures us of something. It is difficult to see of what it would remind and assure an infant. The theology of the question quite closely connects the physical eating and drinking with spiritual eating and drinking, but faith is necessary (“me and all believers”). The consistory has the responsibility to fence the table from unbelievers. The only way they can do that is by profession of faith.
HC Q. 76: again, faith is the focus here: “accept with a believing heart…by believing…united more and more.” Even more directly, this question focuses on the active participation of acceptance.
HC Q. 79: the words “visible sign and pledge” imply that the recipient knows what the visible sign and pledge mean and also that to which they point. The words “in his remembrance” are not crystal clear as to whether the remembrance is active or passive. However, when one looks briefly as Ursinus’s commentary on the question, there is no ambiguity. In fact, he spells out the active requirements of the Lord’s Supper in response to this question.
HC Q. 81: There is no way that a consistory can know whether anyone fulfills these requirements (three verbs here of being displeased, trusting, and desiring) in infancy. The nature of the sacrament is not that it gives benefit whether a person knows it or not (this would be a Romanist position). The benefit is in the active participation. Of course, infants are not in the same category as the unrepentant.
BC article 35: there are several things in this article that point to requirements beyond what an infant can perform. In the first paragraph, we have the words “nourish and sustain.” In the context of an article that continually harps on the mouth of faith, no nourishment happens without cognitive understanding. The article explicitly ties the Lord’s Supper to the second birth, not just the first birth. Even more important is the actual language of reception: “received spiritually by faith.” It is received in no other way. When one remembers that faith includes notitia, then it becomes impossible for an infant to have the maturity necessary to understand what is happening and thus receive the benefit. The article goes on to say that faith is the hand and mouth of our souls. To tie it even more closely to the matter at hand, it goes on to say that “the manner in which we eat it is not by the mouth but by the Spirit, through faith.” Infants, while capable of a seed faith, are not capable of understanding enough to discern the difference between eating by the mouth and eating by faith. To them it is just another piece of bread, and just another drink of wine or grape juice. Furthermore, the article says that the Lord’s Supper “nourishes, strengthens, and comforts” our souls. It is difficult to see how that would apply to an infant. The two paragraphs beginning with “moreover” and “finally” (I am using the CRC translation, by the way) detail the fact that not all receive the Sacrament and the thing signified. The wicked person does not receive the thing signified. The infant is not in the same category as to the reason why he does not receive the thing signified, but it is obvious that not all receive the thing signified. The paragraph beginning with “Finally” details quite a number of things that are supposed to happen when we receive the Sacrament. They are: 1. humility and reverence; 2. thanksgiving; 3. holy remembrance; 4. confess our faith; 5. examining oneself; 6. moved to a fervent love of God and neighbor. All of these things are necessary for the right administration of the Sacrament. Therefore infants are not to participate.