FFXIV Client setting set to read only

[Kirika-]

Make sure the game was installed in it's default install location.
If you are on a Windows PC, make sure the windows account has Administrator privileges, a guest account or a limited account will cause Windows to reject or discard any file changes attempted by the game depending on the privileges set for the account.
If you are on a Windows PC and do have full privileges for your windows account, then in Windows Settings type "Controlled folder access" in the search slot and click the result to access that setting.
Turn off this feature, then see if the game can then save you game client settings correctly.
A few updates back, Windows added and then enabled by default the Ransomware Protection feature in Windows Security. It is a good thing, however, it can and does get "out of sync" with "friendly" programs, especially when those programs get patches and updates. The Ransomware Protection can then sometimes no longer see the program as a "friendly", because it has changed, and then will reject any attempt the program will make to change a file within the Protected folders, of which are the User folders in your windows account and where FF14 stores the local files for the game setting and UI customizations.

As Ilisidi said, it isn't the FF14 game client being the issue, its either your Windows account privileges or Windows Security being stupid, and in most cases, its the latter.