SharePoint Header remove or hide from users

rredford This is not possible using SharePoint out of the box functionality.

Also, it is not recommended by Microsoft to remove the Office 365 banner. You will loose App launcher at the left, search box, site settings (gear icon) & profile settings.

Also, if you want to hide it using CSS, you have to inject the custom CSS on modern pages using SPFx Application customizer. See below post for more information about this:

What is the best practice for getting JS and CSS files into a SharePoint Modern Page? 

You can use the custom CSS something like:

div#SuiteNavWrapper {
    display: none !important;
}

Note: DOM manipulation & CSS customizations are not recommended by Microsoft and some of your customization may break if Microsoft changes HTML element id/classes in new release updates.

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