I assume the "notification settings" there are not granular enough to turn off this notification without blocking email alerts? Worth a check anyway.
The email app might want contacts access so that it can look up (or store?) any contacts' email addresses. That seems legitimate to me. I'd check in the system "accounts and sync" settings (or Samsung's equivalent, as they tend to change all of the menus) to make sure that app doesn't have calendar and contact syncing options, or that they are turned off if it has.
Otherwise I guess you've already checked the app's own settings to turn off anything that might enable at least calendar access (as I say, I would expect an email app to request contacts access). It's likely that it wants this so that it can add events received via email to your (Samsung?) calendar, so it's conceivable there's an option to stop that.
And if nothing else will stop it, I'd find a different email app. If a built-in app doesn't do what you want (including not nagging you about things you don't want) then there's no reason to use it rather than another one of your choice.