Family baptism - and a question

I attended the baptism of a cousin's daughter on Sunday. It had been a while since I'd attended a Presbyterian worship service (the denom of my youth). Apart from a little weirdness of "battling music groups" (choir and organ on one side of the front of the church; guitar, piano and two singers on the other; alternating songs and styles), the service was very nice, with an excellent sermon from an enthusiastic and engaging minister.

I had one beef with the baptism though and I have been trying to determine whether it was done in proper form. After the parents made their promise, "members in good standing of {Name} Presbyterian Church" were asked to stand and make their promise, and then recite the Apostles Creed. That left all other Christians in the sanctuary, including Catholics, Baptists, Pentecostals, many of whom are very closely related to the child, sitting in their seats. It just felt so divisive to the Body of Christ.

I don't remember the promise as being anything other than to support the parents in raising the child in the faith, and so I don't understand why others who care for this child couldn't make the promise. Does anyone know if this is usual?