The construction of "to be accustomed to not talking" sounds awkward. This is because the verb "to be accustomed to" is a very quirky and awkward verb to employ, and requires a gerund (the noun form of the secondary verb, such as "walking", "talking" etc.). It is awkward when used in the negative.
If the verb were almost any other verb, for example "prefer", we find that both the negative and the affirmative forms of the verb are comfortable.
In formal English, the infinitive form of the verb must not be split. The infinitive form of the verb "glance" is "to glance". In other words, "to glance quickly" is correct, but "to quickly glance" is not.
"They preferred to talk at meals." No problem.
"They preferred not to talk at meals." No problem.
"They preferred to not talk at meals." Incorrect.
So, it is actually the usage of "be accustomed to" which presents the problem.