How so? I don't remember ever having seen issues with this. If anything CSP steers you towards this (instead of inline scripts directly assigning to JS variables)
CSP blocks execution/inclusion, but since json does not execute and any json mimetype will not do execution there is no problem.
Any CSP-allowed other script can read that application/json script tag and decode it, but it is no different than reading any other data it has access to like any other html element or attribute.