[Ayantir]

Messages are based on the ID of the sound sent to the UI, maybe :

SOUNDS.ABILITY_TARGET_IMMUNE = SOUNDS.NONE

Server will send SOUNDS.ABILITY_TARGET_IMMUNE code, but because in UI the value isn't the same, it won't be displayed..
PS : It will also won't play the sound

If you want sound and not message, perhaps :

function ZO_RecentMessages:ShouldDisplayMessage(message)
    self:Update(GetFrameTimeMilliseconds())
 
    if(message == SOUNDS.ABILITY_NOT_ENOUGH_STAMINA or message == SOUNDS.ABILITY_NOT_ENOUGH_MAGICKA or 
        message == SOUNDS.ABILITY_NOT_ENOUGH_ULTIMATE or message == SOUNDS.ITEM_ON_COOLDOWN or
        message == SOUNDS.ABILITY_WEAPON_SWAP_FAIL or message == SOUNDS.ABILITY_NOT_READY or
        message == SOUNDS.ABILITY_TARGET_OUT_OF_LOS or message == SOUNDS.ABILITY_TARGET_OUT_OF_RANGE or
        message == SOUNDS.ABILITY_CASTER_SILENCED or -- message == SOUNDS.ABILITY_TARGET_IMMUNE or 
        message == SOUNDS.ABILITY_CASTER_STUNNED or message == SOUNDS.ABILITY_CASTER_BUSY or
        message == SOUNDS.ABILITY_TARGET_BAD_TARGET or message == SOUNDS.ABILITY_TARGET_DEAD or
        message == SOUNDS.ABILITY_CASTER_DEAD or message == SOUNDS.ABILITY_NOT_ENOUGH_HEALTH or
        message == SOUNDS.ABILITY_FAILED or message == SOUNDS.ABILITY_FAILED_IN_COMBAT or
        message == SOUNDS.ABILITY_FAILED_REQUIREMENTS or message == SOUNDS.ABILITY_CASTER_FEARED or
        message == SOUNDS.ABILITY_CASTER_DISORIENTED or message == SOUNDS.ABILITY_TARGET_TOO_CLOSE or
        message == SOUNDS.ABILITY_WRONG_WEAPON or message == SOUNDS.ABILITY_TARGET_NOT_PVP_FLAGGED or
        message == SOUNDS.ABILITY_CASTER_PACIFIED or message == SOUNDS.ABILITY_CASTER_LEVITATED) then
        return true
    end
    
    if message == SOUNDS.ABILITY_TARGET_IMMUNE then
        return false
    end
 
    if(self:IsRecent(message)) then 
        return false 
    end
 
    self:AddRecent(message)
    return true
end

But it's a dirty one! Untested, not at home, let's try?