I'm running Mojave 10.14.2 and for some reason messages wasn't allowing me to block people. They were already blocked on my iPhone but going to the block screen showed nothing. When I tried blocking somebody it would not add them. I found out that if I blocked them in FaceTime it would transfer over to messages, kind of strange. I'm assuming this is a glitch that hopefully gets sorted out.
MacBook Pro Retina (2015 and later)
Good morning cichlid81,
Welcome to the Apple Support Communities!
I understand you are trying to block some people in the Messages app. Are these the steps you were taking? Were you having this issue with all of the numbers you tried to block in Messages, or only a few individuals?
Block phone numbers and contacts on your iPhone, iPad, or iPod touch
"There are a few ways that you can block a phone number or contact.
Messages
If you're in Messages, open the conversation, tap the contact at the top of the conversation, then tap 
Tap the name or phone number, scroll to the bottom of the Info screen, then tap Block this Caller.
Phone
If you're in the Phone app under Recents, tap
next to the phone number or contact that you want to block. Scroll to the bottom of your screen, then tap Block this Caller.
FaceTime
If you're in the FaceTime app, tap next to the phone number or contact that you want to block. Scroll to the bottom of your screen, then tap Block this Caller.
When you block a phone number or contact, they can still leave a voicemail, but you won't get a notification.
Messages that are sent or received won't be delivered.
Also, the contact won't get a notification that the call or message was blocked.
You can use some third-party apps to detect and block spam phone calls."
Take care.
Workaround For macOS messages
