I went back and watched the scene again, and he is wearing a rosary. As Ritsuko says that's not common; I wondered if it was hers Sentaro was wearing.
We all carried our rosaries in little plastic pouches in our pockets. Nuns sometimes wear them hanging from their waists, but I don't recall any parish priests who did that. I was an altar boy and attended Catholic school for a good chunk of my childhood, so I think I would have noticed. It wasn't uncommon to wear a crucifix hanging from a chain or string around one's neck, a common symbol of Christian belief in anime, but never a rosary.
Spoiler for rosaries:
For those unfamiliar with rosaries, it's a
prayer tool consisting of five lengths of ten beads separated by spacing beads, with a part that hangs down at the bottom with five beads and ending with a crucifix. The rosary begins by holding the crucifix and reciting the "Apostle's Creed," a shortened version of the
Nicene Creed that first codified the basic beliefs of Catholicism in 325 CE. The rest of rosary consists of reciting the "Our Father" and "Glory Be" prayers on the spacers, and the "Hail Mary" on the rest. It ends with the "Hail, Holy Mary" prayer. I don't recall learning about the various "mysteries" described in the linked article though. I do recall having to say the rosary on the school bus whenever the nun riding with us decided the children had become too rowdy.
Now that I watched it again, I can see how, from his reaction to Ritsuko's comments about their priest, Sentaro might be considering a vocation in the priesthood. Maybe wearing a rosary about the neck is a Japanese Catholic practice, or maybe just an invention by the writers. (The script for episode two is by Kakihara Yuuko; I can't find any biographical information about her via Google.)