Some people are blocked

Sometimes you have to sign out and back in for the changes to take affect

Yes but I do not want to block everyone but I nor do I want to receive messages from friends only. The purpose of LIVE is to be able to communicate with people, I just don't enjoy the sarcasm and hate filled messages when you beat someone in a game.

You can change who you want the notification to appear in the settings.

Thanks for the reply but no... not the case. I've tried everything . This is only a problem in the last few months and Xbox suggested they might have a bug in the system bc I even tried it with them. Anyone I block can continue to send me messages and
it's beyond annoying ..

Block another player

Blocking another player prevents you from receiving that player’s messages, game invites, and party invites. It also prevents the player from seeing your online activity and removes them from your friends list, if they were on it.

1. Press the Xbox button
   on your controller to open the guide.
2. Select People, and then select the gamertag of the player you want to block.
   Note If the player is not on your friends list, select
   Recent players or Find someone and enter the player’s gamertag to search.
   
3. From the player's profile, select Report or Block, and then select
   Block.

Mute or block another player