How do I hide a contact without deleting them?

Open the contact and tap "Dismiss." You'll pick how long to dismiss them for (1 week, 1 month, 3 months, 6 months, or 1 year). The contact disappears from your active lists for that period and then comes back automatically when the time is up. If notifications are enabled, you'll also get a reminder when they reappear, so dismissed contacts won't quietly slip through the cracks. You can find or restore dismissed contacts at any time from the link at the bottom of your Contacts list, the ••• menu in Contacts, or Settings → Dismissed Contacts.