There has been vigorous discussion here on meta about the new Code of Conduct and its requirements regarding pronouns. The discussion has been exclusive to third-person singular pronouns, but nothing in the CoC or the associated FAQ explicitly restricts to the third person or to gender. This raises the question of how it applies to second-person pronouns.
For example, suppose a user indicates that their preferred second-person singular pronouns are thou/thee/thy/thine/thyself instead of you/you/your/yours/yourself. A literal interpretation of the CoC ("Use stated pronouns (when known).") indicates that all other users are obliged to (actively) use these pronouns when addressing that user.
This particular example may seem archaic and therefore unlikely to come up, but thou is still used in a handful of regional dialects of English. Also many other modern languages commonly use equivalents for both you and thou. Deciding which to use is a notorious social challenge in languages that use both, as it can lead to mild offense if the wrong one is used. Thus I can easily imagine such an issue arising on a non-English site (although the question is valid for English too).
Another example to consider is a user requesting to be addressed in the third person, rather than the second person. That is, instead of "you should restart your computer" the preferred language is "OP should restart their computer". Again, this request is not so strange; avoiding the second person is standard in many formal settings, such as in parliament or in court. Failing to comply with such a request would be avoiding the use of gendered third-person pronouns, which seems to violate the CoC.