I guess your question is referring to the different spaces: role-ational space vs. relational space. Whereas Holacracy provides a great framework to solve tensions within role-space (eg creating clarity via governance etc.) and that definitely has a side-effect on how people show up (it feels to me as boost for personal development) it does not provide tools to address relational issues (e.g. I don't like to way you are talking to me as human being or how you criticize me ongoingly etc...).
In fact Holacracy does not and is not meant to support people in leading challenging conversations or providing feedback. It's focus is clearly on the organzational (role) space. Thus I see a strong need to build up individual skills in how we interact as human beings (may it be verbal aikido, non-violent communication, awareness practices or whatever feels appropriate and helpful...). I would typically integrate that in the process of transitioning an organization to Holacracy.