On my MacBook (latest OS), if I want to log into my Office 365 email, via Safari, I am presented with the image below, despite selecting the box "Don't show this again", it presents itself each time I go to log into Office 365.
The "don't show" box works for me (mostly: it does pop up again occasionally but it's not every time). Do you have any extensions installed that might be conflicting with it?
Another setting to check is "Prevent cross-site tracking". Basically, it's trying to store a cookie somewhere, and later it can't find it, so you get to go through the routine again.
Another setting to check is "Prevent cross-site tracking". Basically, it's trying to store a cookie somewhere, and later it can't find it, so you get to go through the routine again.