The Magen Avraham in 166 SK 2 brings the Maharshal in his Tshuvos #34 that if one is waiting after netillas yadayim for the rest of the group to finish washing in order to make hamotzi, and he is asked a Torah question, it is a sin to sit silently. You should talk words of Torah, and you should not worry about interrupting between Netillas Yadayim and Hamotzi. The Maharshal explains that since it is meritorious to say Divrei Torah at a meal, divrei torah should be considered a direct necessity of the meal. Talking about things that are necessary for the meal is not a hefsek.
The Magen Avraham brings that many poskim disagree with the Maharshal and do prohibit talking in learning after netillas yadayim. The Maharshal himself actually holds that talking is not prohibited, only discouraged, and this might be the basis of his hetter. That is, if the Maharshal held that hefsek was a real problem, he probably wouldn't have been mattir just based on the mishna in Pirkei Avos. And even the Maharshal only says that if you are asked a question, you should answer. He doesn't say that you should bring a sefer and arrange a chavrusa for after netillas yadayim while the rest of the yeshiva is washing.
The halacha might not be like the Maharshal, but I like the idea anyway. A meal without Torah is like zivchei meisim; divrei torah are necessary to change the meal from an animalistic and vulgar necessity into a holy and beautiful experience; therefore, Divrei Torah are a vital part of the meal; therefore one may talk in learning after netillas yadayim.
Speaking of the Maharshal-- the Maharshal, Rav Shlomo Luria, had a close relative - depending on what you read either a cousin (sheni be'sheni) or a nephew (rishon be'sheini) - named Reb Moshe. This Reb Moshe, also known as Moshe Issreles, wrote the Rama. While the Maharshal was very critical of the Rama (see Tshuvos Rama #7 for the Rama's response) for writing (HASKOOOLISHE SFOOOREM!) about Aristotelian philosophy, he had, in general, a high opinion of the Rama, as do most of us. The Rama in OC 98:1 brings that one should not kiss his little children in shul, in order to inculcate in them that even his great love for them does not come before the love of Hashem. I believe that this restriction only applies to "Banav haktanim," i.e., 1. his children, and 2. who are little. Not banav? OK. Not ktanim? OK.
This does not mean that it is OK to lean over the mechitza to kiss your neighbor's spouse, which used to happen every Shabbos at a certain Orthodox shul I attended many years ago. Although Frost used the expression "Good fences make good neighbors" ironically, sometimes davka good neighbors need good fences.
In the interest of honesty, here are two poskim, among many, that disagree with me: The Yechaveh Da'as and another posek. And, closer than Morocco and the Eida Chareidis, Eli in the comments also takes issue with this, although I disagree with his raya from the Darchei Moshe and the Binyamin Ze'ev. And here's a tshuva from the Pnei Meivin of Munkatz, who doesn't want to commit on the issue.
On the other hand, Harav Reuven Feinstein did tell me that he holds, as I said, that the issur is only on Banav, which involves a level and type of love completely different from the love you have for friends and teachers or even brothers. The additional point that I made that the issur is limited to banav haktanim is mine, and I did not hear it from him.
Again speaking of the Maharshal, Rav Yosef Karo and the Maharshal were contemporaries, and they engaged in a great deal of halachic correspondence. There is an interesting minhag mentioned by Rabbi Karo in Shulchan Aruch Orach Chaim, as I will explain.
There's a story about Congregation Kehilath Jeshurun, a shul on the Upper East Side of Manhattan commonly known as KJ, that gave a guest the honor of Gelila, the wrapping and covering of the Torah. The rabbi, Rabbi Haskel Lookstein, discerned that the man was completely unfamiliar with the procedure, so he carefully and discretely instructed him step by step, and he managed to do it correctly. After the gelila was finished, Rabbi Lookstein, relieved to have smoothly handled the problem, handed the atarah, the crown of the sefer, to the honoree, who looked at it for a moment, shrugged, and put it right on his own head. This story is often used as a cautionary tale to young rabbis to never, ever assume any knowledge at all on the part of baalei batim. Something might be obvious to you, but if you don't make it crystal clear to the baalei batim, it will be misunderstood. However, it's worth knowing that in OC 154:10 the Mechaber brings that in some places, they had a minhag to place the Atara on the head of the Chassan Torah, the person who is honored with the last aliyah on Simchas Torah. The Mechaber adds that one may not extend this minhag to chassanim (unless special arrangements were made when the atarah was purchased, see Taz and MA.)
So Rabbis, although this is not likely to ever happen any more, because our ataros usually have tubular sheaths for the Atzei Chaim, and so the crown would not fit on a person's head unless he had horns, if this ever happens in your shul, remember the minhag the Mechaber brings, and use it to alleviate the mortifying embarrassment which was your fault for not preventing it in the first place.
I was just told by a talmid chacham and ish ne'eman that his father, who was gabbai in a shul in Cincinnati in the sixties, told him that this happened in his shul-- that the guy put the atarah on his head after gelilah. My informant says that he does vaguely remember this happening, but he was a young child at the time so his memory is not clear.