There are some people who don't like to take food (with chopsticks) from the same dish (as everyone else)
There are some people who don't like sharing food from the same dish
(so that's why) we have separate chopsticks for taking food from the shared dish(pot/plate) and for eating
「同じ鍋をつつきあうのを嫌がる人もいる」＝ There are some people who don't like to take food (with chopsticks) from the same dish (as everyone else) / There are some people who don't like sharing food from the same dish
「（だから）よそう用の箸と食べる用の箸が分かれている」＝ (so that's why) we have separate chopsticks for taking food from the shared dish(pot/plate) and for eating
ボキャブラリー
「鍋」＝ pot / pan
「つつきあう」＝ to take food from the shared dish (using chopsticks)
「箸」＝ chopsticks
「分かれる」＝ separate / use separate ～
イギリス 
