You can use the On Damage: Event to check when an entity takes damage, and then use victim is a player to make sure that the entity is a player...

As for setting the player's team, you can make a variable like {%player%.team}, then assign the team of a player with:
set {%player%.team} to *the team you want them to be on*

Finally you can check the team on the damage event with {%victim%.team} is {%attacker%.team}, and then run the cancel event effect to stop the damage!

 

You have the right idee in mind but it's executed very poorly

 

Those variables though...

1. Do not start off your variables with expressions.
2. Do not use nested variables. Use list variables instead. (https://skripthub.net/tutorials/43)

Code (Text):

1. {%player%.team} -> {team::%player%}