I revoked Contacts access in WhatsApp a year ago. It works just fine. Problem is: WhatsApp only shows the phone numbers in the list and NOT the usernames of people. This is rather annoying, because I don't know any phone numbers by heart. Profile pics help a bit, but people change them and often don't have pictures of themselves.
Signal shows the nicknames next to the numbers which is a really nice feature and makes it pretty much perfectly usable without contacts permission, except that it constantly nags to grant the permission.