The browser can be set to block all cookies but it will break a lot of sites from working.

There are extensions that will delete the cookies from a site when you load another site, or close the tab. Those are pretty good. You can whitelist the sites where you want cookies to exist so you dont have to login all the time.

Like this one: https://addons.mozilla.org/en-US/firefox/addon/cookie-autodelete/

Cookies are just files stored on your computer. You just need to forbid the site from saving anything - done (all major browsers support this in some form).