For me this works only to stop future messages from that campaign. All the campaigns seem to buy and sell lists so I just get a different message from a different campaign at a different number. Here are the most recent offenders:

  Katrina Christiansen
  Harry Dunn
  Arizona for Abortion Access 
  Turnout PAC
  Yvette Clarke
  Josh Stein
  Ty Pinkins
  Democratic Majority
  Tammy Baldwin
  Democrats United

Yes this was my experience too. It was like a hydra. Say no to 1 campaign, get 2 more new campaigns tomorrow

For political messages, this doesn’t work—they ignore it. It just validates that you saw the message (and rewards the behavior).

If the messages are automated this works and is legally required. Many political messages may be a template but come from real humans. It's a way around the law.

Human pushes the button so it's not a machine.

Does it still count if a human is supervising an autoclicker?

Call from another jurisdiction, and good luck trying to enforce any laws.

Back in the old days spam call centers were often in the Caribbean for that reason, but now that phone calls are so cheap, they might be anywhere.

This is why I don’t answer any calls from a number I don’t know. It just validates to a potential spam system that my number belongs to a real person.

Exactly. Which I have tried to explain (unsuccessfully, alas) too many times. We only answer calls from numbers we recognize.

This has caused some interesting issues, though. My wife answered one of the unknown-callers on her cellphone anyway, and it turned out to be from her doctor's office. Who couldn't (or wouldn't) explain why the clerk was using per personal cellphone to call patients, or how they got the number. We still maintain a land line, and only eight individuals have my cellular number, only five have hers. Yet somewhere a dataset was purchased, and both our cellular numbers have propagated throughout the Electronic Medical Records system, often as the only contact number.

This works for me too with Verizon. And on iOS, under Settings > Messages, I enable "Filter Unknown Senders".