I have a super weird behavior with my site. I can login once if cache has been purged.
Clear what cache? You mentioned caching was already turned off.
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La session a expiré ou les cookies ne sont pas activés par votre navigateur. Veuillez cliquer sur "Actualiser" et vous assurer d'avoir bien activé les cookies dans votre navigateur.
The CSRF token is being rejected then. This is generated and validated by Joomla. Are you having this issue with any other forms? Be sure your CB Login Module does not have caching enabled as you cannot cache forms due to their CSRF tokens.