Unfortunately there is no single way that would work for all the political text messages but here are some tips and it may require using more than one option.
- Block caller if they come from the same number
- Some text messages require you to text a number or message to a different number to stop communication. Capitalization counts when replying. If the say to send "STOP", then "stop" may not work. You may have to continue to do this as you could be on many lists that you need to be removed from.
- Contact each politician and have them remove you.
- They use a central database of names and numbers to target robo-texts and calls. If you could get removed from that list, it would stop a large number of them. Getting the name of that list may be difficult and they do not make it easy to contact them unless you are wanting to donate. Here is one such database they use with no clear way to remove yourself, but you may be able to dig deeper:
https://www3.gopdatacenter.com/rnc/Login/Login.aspx
- You can review FCC rules for political communication and file a complaint.
https://www.fcc.gov/rules-political-campaign-calls-and-texts
- Filter all unknown senders can be used, but this will filter all texts from anyone not in your Contacts and put them in a separate folder. This is only available when sent using iMessage.
Block, filter, and report messages on iPhone - Apple Support
- Report as SPAM to your carrier.