Quickly remove blocked phone and email contact entries
Tahoe update:
Apple has moved the blocked contacts setting. It's now in the System Settings, and is also now far easier to remove selected entries.
This does still require macOS as there is no method in iOS that doesn't require removing entries one at a time.
Go to System Settings > Privacy & Security > Blocked Contacts
Click on Blocked Contacts. You'll first see a line simply showing how many blocked email and phone number entries you have. Presently 101 in my case.
Click on that top line and a list of all entries will appear.
From here, you can choose the entries the same way you would from a list of files and folders in the Finder. Click on any one and then Command+A to select them all. Select one and then Shift+click anywhere above or below to select/deselect a contiguous set. Or Command+click to add/remove single entries in any order.
Click the minus button at the bottom left of the list to remove all selected items.
Previous to Tahoe:
When you have a long list of blocked phone and email contacts to remove on your iPhone, iPad or Mac, this is quite a chore when done on an iPad or iPhone as Apple does not give the user a way to remove multiple contacts at once. They have to be done one at a time.
This method still requires removing entries one at a time, but is much, much faster. The only caveat is that it requires a Mac to proceed.
Since Messages is automatically on for syncing with iCloud, the assumption is this feature is already enabled on all of your iOS devices.
On your Mac, open Messages. From the top menu bar, choose Messages > Settings. Or, press Command ,
Click the iMessage tab at the top center of the palette. If necessary, sign in with the same Apple ID and password your iPhone and/or iPad is using.
The most important thing to do here is to make sure the check box for Enable Messages in iCloud is on so the changes you make here propagate to your iOS devices.
Next, click the smaller Blocked tab. Click the top item so it's highlighted. At this point, you can now rapidly click the - (minus) button to remove even hundreds of entries in just a few moments.
You won't notice this change instantly on your iPhone and/or iPad. Give your iOS devices up to a minute or so to match what you did on the Mac.