Cambridge records “accuse someone of something” and specifically “accuse someone of doing something.” That supports of + -ing when the action is the alleged wrongdoing.
Cambridge records accustomed to something and gives -ing examples such as being accustomed to working or being treated in a particular way. Do not interpret the “to” after accustomed as an infinitive marker in this construction.
Cambridge distinguishes adapt to a situation or activity from transitive patterns such as adapting plans to fit new circumstances. The surface sequence “adapt … to + verb” therefore needs its grammatical structure identified before choosing an -ing form or infinitive.
Cambridge distinguishes “apologize to someone” from “apologize for something/doing something.” You can combine the two roles, as in “apologize to someone for doing something”; “to” marks the recipient while “for” marks the reason.
Cambridge distinguishes intransitive “approve of” for a favorable opinion from transitive “approve something” for official acceptance or authorization. The official-authorization sense uses transitive “approve” with an object; do not collapse that separate sense into the “approve of doing” judgment pattern.
Oxford documents the person-action pattern as be banned + from + -ing and separately documents direct-object uses of ban. The cited evidence does not support person + to-infinitive as the equivalent prohibition construction.
