I've used "Forward Text Messages" for years to send SMS from macOS. Since last week, names of "SMS people" are marked RED in Messages, and I can't send SMS from macOS anymore.
I've updated to the latest iOS and macOS, logged out and in of iCloud on both devices, and flicked "Forward Text Messages" in Settings off and on several times, to no avail.
My only lead is that when flicking the setting, I'm supposed to be asked to enter a code (on the Mac, I think), but this does not happen. Apple Store had no idea and I've found no help on the Web.
Clicking on the red name shows this context menu:
✔︎ (number) iMessage (Ghosted)
(number) is not registered with iMessage (Ghosted)
Remove (name) from chat
Show contact card
Also, the message field at the bottom shows "iMessage", where it said "Text message" before.
SMS sent from iOS are added to messages on macOS. So it works that way, but not from macOS to iOS (because Messages does not seem to know about SMS, only iMessage.)
NEW: Turned "Forward Text Messages" off, turned off both Mac and iPhone, turned both on, and turned "Forward Text Messages" on. I get no question about entering a code, and still RED names.
Best Answer
On your iPhone, do you have an email address checked under settings>Messages>"send & receive"?
for some reason, it only works when I have an email address checked which was not the case before. They must have changed something on their end to require the use of an email.