Question: My son came back from Yeshiva claiming that he learned that one may talk in shul while the haftara is being read. Is he right?
Answer: Rabbeinu Yerucham (Toldos Adam Vechava 2:3) writes that as the haftara is read for everybody in shul, one must not speak while it is being read. The Shulchan Aruch (OC 146:3) writes that one must not talk until the haftara has finished being read, just like kerias hatorah.
The Avudraham suggests a few reasons as to how the haftara got its name. One suggestion is that it was used to exempt (pattur) the community from kerias hatorah during times of persecution when they were prohibited to read from the Torah. Alternatively, he writes, quoting Rabbeinu Tam, that one is forbidden to speak at all during kerias hatorah, even in halachic matters. Once the Torah has been wrapped back up and they have begun reading the haftara, they are allowed to open their mouths and speak again (peter means to open).
The Levush (OC 284:1) challenges this explanation, writing that as everyone is obligated to listen to the haftara, then clearly one cannot speak then. Rather, one is allowed to speak, specifically to clarify halachic issues, such as a mistake in the reading. Such talking one may only do while the haftara is being read, but not during kerias hatorah.
The Pri Megadim (Mishbetzos Zahav OC 284:1), however, disagrees with the Levush, writing that as the Shulchan Aruch compares the haftara to kerias hatorah, one cannot even talk about halacha while the haftara is being read.
In conclusion, one must not talk at all while the haftara is being read.
In loving memory of Sholom Mordechai ben Tzvi