Being a Firefox user, I have set dom.event.contextmenu.enabled and dom.event.clipboardevents.enabled set to false, so that I can continue right-clicking and pasting.
If you are on macOS, I have two Services I use to get around these.
Paste as Keyed Characters types in the contents of the clipboard for you [0].
Paste AlphaNumeric Only will only paste in letters and numbers from the clipboard [1]. Very useful when pasting contact phone numbers into forms that only allow numbers.
You do not end up losing those. Both the popup menus - the site's as well as the browser's - are shown, the latter on top of the former. Press Esc to make your browser's vanish, and you still have the site's available.