To "fit in" and hide that he is a Jew
While I haven't read the book and I don't know the exact circumstances, the OP in his own answer was right that since the late 1950s there was a steady grow of anti-Semitism in Poland, which indeed has culminated in the forced emigration of Polish citizens with Jewish roots after the events in the March of 1968.
In the 1950s, the Polish culture was very open towards the Jewish minority: Poland was one of the biggest source of Jewish books and the Cultural Society of Polish Jews was very active. The death of Stalin in 1953 and the events of "Polish October" (1956) was promising the democratic changes including greater autonomy from USSR and reduction of censorship. The promise didn't last long and the quickly gained freedoms were being reversed over the next few years.
Already in 1956, the Cultural Society sent a letter to the Party (the Polish United Workers Party) presenting their concerns that "there are elements within the Party that are trying to blame the Jews for the terror committed during Stalin's rule". Initially, the Party has responded by declaring that there is no place for such anti-Semitism since Poland is a home for many cultural minorities and none of them should be discriminated.
In 1960 a new, informal faction was created within the Party (called "The Partisans") made mainly from the ex-soldiers (both from the regular army as well as from the partisans fighting during WW II). They were pointing that while they were fighting the Nazis, lots of the "old Party members" (which included many Jews) were hiding in USSR and were later supporting Stalin's terror. The Partisans were controlling the Ministry of Internal Affairs (which included the secret police) and they have started invigilating Jewish organizations.
On the 5th of June 1967, Israel has started the Six-days war. In response, the Soviet Union has broken diplomatic relations with Israel and in Poland started organizing protests against the "Imperialistic Zionists". The First Secretary of the Party accused Polish Jews of working against Poland, comparing them to the infamous "Fifth Column", conspiring with Germany to reverse the post-war Polish western border changes (while Poland has lost large regions on the east, it has gained important previously German lands like Eastern Prussia and Lower Silesia). People with Jewish descent were getting removed from important positions within the army, police and universities.
On the 25th November 1967, the National Theatre presents a play based on probably most important Polish poem - Dziady Part III by Adam Mickiewicz, written in the XIX century and dedicated to the students persecuted after the failed 1830 Polish uprising against tsarist Russia. Polish government declares it as "anti-Soviet" (contrary to the initial positive reviews in the Russian Pravda) and started pressuring the theatre to reduce the number of plays, banning it finally on 30th January. Students and writers started protesting, demanding freedom of speech - those protests were violently attacked by "workers" (plainclothes police) and by the anti-riot police. In response, the Party has created its own "spontaneous workers demonstrations" which were demanding that "students should go back to schools and Zionists to Zion". According to the speech by the First Secretary, Jewish students and teachers were responsible for the protests - afraid that this will turn into another Prague Spring, the government decided to find the scapegoat and punish them harshly. Those with Jewish heritage were the perfect fit.
In the aftermath of the events (called often March 1968), the Party has forced between 13 to 20 thousand Poles with Jewish heritage first to quit their jobs, then, after stripping them from the Polish citizenship, to leave the country.
Now, what has this to do with the characters from the novel?
If Beniek was a Jewish boy growing in the increasingly anti-Semitic country, he would try to fit-in hiding his Jewish culture (the anti-Semitism has much more to do with the culture than with the religion). This would include going to the preparation for the First Communion - while Poland was indeed a Communist (so in theory - atheistic) country, the Party wasn't openly fighting with the Catholic Church, noticing its important cultural role. So while a prominent party member would be asked to "stop believing in the Church nonsense", the average citizen was free to go to church and send kids to First Communion/Confirmation etc.
There is a great poem/song called "The story of one emigrant" that describes a story of a Jew in post-war Poland