Google Apps Script - Editors Execute Script on Spreadsheet

If, as you stated in comments, you use an installable on Edit trigger the problem you describe should not occur since "When a script runs because of a trigger, the script runs using the identity of the person who installed the trigger, not the identity of the user whose action triggered the event. This is for security reasons. For example, if you install a trigger in your script, but your coworker performs the action that triggers the event, the script runs under your identity, not your coworker's identity. For complete information on this, see Understanding Permissions and Script Execution."

see doc here

EDIT : sorry, I didn't see the issue about this special case : issue 1562 posted on july 2012, status "triaged"

EDIT 2 : I tried @tracon6 suggestion to remove the protection temporarily but it doesn't work either... the script generates an error when trying to apply the protection.

but

as an EDIT 3

I found a workaround that works ! We can add an editor just for the time we write to the targetSheet and remove it right after... using a flush in between it works.

here is the code I used to test :

function onEditInstallable(event) {
  var sheet = event.source.getActiveSheet();
  if(sheet.getName()=='Sheet1'){return};
  var r = event.source.getActiveRange();
  var column = r.getColumn();
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var targetSheet = ss.getSheetByName("TFA");
  var targetSheet = ss.getSheetByName("Sheet1");
  var user = SpreadsheetApp.getActive().getEditors()[1];
  var permission = targetSheet.getSheetProtection();
  permission.addUser(user);
  targetSheet.setSheetProtection(permission);
  SpreadsheetApp.flush();
  targetSheet.getRange(1,column).setValue('value change on sheet 2, column  : '+column);
  SpreadsheetApp.flush();
  permission.removeUser(user)
  targetSheet.setSheetProtection(permission)
}

EDIT 4 :

Since it seems that many editors could have access to these sheets (see last comments), there has to be a way to know who is active on the spreadsheet. In a non domain environment this is not possible with a triggered function so I would suggest a small uiApp with a list from which the user has to choose, trigger that with an installable onOpen and store the value to use it in the main function.

Heres is a piece of code to handle that aspect.

function SpecialonOpen(){
  var s = SpreadsheetApp.getActive();
  var app = UiApp.createApplication().setTitle('Please select your email in this list').setWidth(300).setHeight(300);
  var list = app.createListBox().setName('list')
  var editors = s.getEditors();
  for(var n in editors){
    list.addItem(editors[n].getEmail());
  }
  var handler = app.createServerHandler('getMail').addCallbackElement(list);
  var btn = app.createButton('select',handler);
  s.show(app.add(list).add(btn))
}

function getMail(e){
  var email = e.parameter.list;
  var editors = ScriptProperties.getProperty('currentEditors')||' ';
  if(editors.indexOf(email)==-1){
    editors+=(','+email);
  ScriptProperties.setProperty('currentEditors',editors);
  }
  var app = UiApp.getActiveApplication().close();
  var editors = ScriptProperties.getProperty('currentEditors').split(',');
  if(editors[0].length<2){editors.splice(0,1)};
  Logger.log(editors)
  return app
}

You should also add a function to reset this list at some moment... don't know what would be best ? on a daily base maybe ? I'll let this to you ;-)