You should be able to do that in Private Browsing, for a single session.

• see Private Browsing - Use Firefox without saving history

That will not retain the login status after the session ends. Also some sites will not remember your login status, and some will time out fairly quickly if there is no activity.

A detail like a website remembering you (log you in automatically) is stored in a cookie.

You can use these steps to make a website remember and recognize you:

• Create a cookie 'allow' exception to keep such cookies, especially in case of secure websites and when cookies expire when Firefox is closed.
• Tools > Options > Privacy > "Use custom settings for history" > Cookies: Exceptions

In case you use "Clear history when Firefox closes" or otherwise clear history.

• do not clear the Cookies
• do not clear the Site Preferences

• Tools > Options > Privacy > Firefox will: "Use custom settings for history": [X] "Clear history when Firefox closes" > Settings
• https://support.mozilla.org/kb/remove-recent-browsing-search-and-download-history

• Clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, passwords, and other website specific data.
• Clearing Cookies will remove all specified (selected) cookies including cookies with an allow exception that you would like to keep.