It's technically against the ToS to use a 3rd party tool like a parser.

That being said, as long as you do not talk about parsing with random strangers in-game, or use parsing results to harass other players, then you should not get banned for using it. Everyone and their mother parses, so do not be scared to using programs like ACT, LogRepV2 or FFXIV-App (which I advise against using due to a specific widget). Everyone discusses parsing results on these forums without bans now... Wasn't like that a year ago unfortunately.