Client side blocking (by that I mean removing them after the tab/page close)? First for third party cookies, then for all of them, and add a "button" next to the url bar, to enable cookies for that specific site (to allow logins).
In contrast, the GDPR does not place requirements for cookies if they're not used for storing or processing personal data (the ePrivacy directive which I'm less familiar with might require a notification about them). It does not even require a popup or user's confirmation if personal data is processed on a legal basis other than consent (though these uses may need to be listed in some kind of available privacy policy document). Finally, as GDPR is mostly technology agnostic, its requirements remain the same regardless of whether the data collection is done using cookies or any other means.