How can I disable text selection using shift without disabling all text selection?

That will bind on document an event where it disables text selection upon pressing DOWN shift

 document.onkeydown = function(e) {
  var keyPressed = e.keyCode;
  if (keyPressed == 16) { //thats the keycode for shift

    $('html').css({'-moz-user-select':'-moz-none',
       '-moz-user-select':'none',
       '-o-user-select':'none',
       '-khtml-user-select':'none',
       '-webkit-user-select':'none',
       '-ms-user-select':'none',
       'user-select':'none'
    }); //or you could pass these css rules into a class and add that class to html instead

    document.onkeyup = function() {
      //here you remove css rules that disable text selection
    }
  }
}

Hopefully i have helped you.

Based on comments

document.onkeydown = function(e) {
  var keyPressed = e.keyCode;
  if (keyPressed == 16) { //thats the keycode for shift

    $('html').addClass('unselectable'); //unselectable contains aforementioned css rules

    document.onkeyup = function() {
       $('html').removeClass('unselectable'); //and simply remove unselectable class making text selection availabe
    }
  }
}

Another solution you might consider: instead of preventing text selection by watching for shift keys and toggling selectability, you could just clear the text selection.

window.getSelection().removeAllRanges();

I find this more convenient because it can be run in your click handler to "cancel" the default behavior. Appears to work in IE 9+ and other modern browsers.