Check out this thread.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
To stop the alerts on a Droid3 go to All Apps and find the Emergency Alerts app. Open it and then click on Menu and Settings. Click on Receive alerts and choose which ones you want. That gets rid of the new annoying behavior.
On older android phones, open Messages, touch the menu button (on bottom left of your phone) and then touch settings. The alerts are there for Presidential (cannot be disabled), extreme alerts, severe alerts and amber alerts. Took me two days and the assistance of Verizon Wireless cust service (about 30-40 min on phone) to figure that one out! GEEEZ!
I've have an HTC Rezound for 4 months. I never had the Severe Weather Alerts until recently. I think the (VERY ANNOYING) weather alerts started after I upgraded to ICS because I know that I didn't intentionally activate them.
tamahat73's solution solved the problem for me. I didn't even realize that there was a menu under Messages. I don't think I would have ever found the solution on my own.
tamahat73 - Thanks for your post! I can once again bring my phone with me into a meeting.