$(document).ready(function(){
  var $btn1 = $("#btn1");
  var $btn2 = $("#btn2");
  var active1 = true;
  var active2 = false;

  $btn1.click(function(){
    $active1 = false;
    $active2 = true;
    alert("after btn1 click: --> " + " active1: " + active1 + ", active2: " + active2);
  });

  $btn2.click(function(){
   // If clicked first on btn1 I'm expecting active1=false; active2=true; ??
        alert("after btn2 click: " + " active1: " + active1 + ", active2: " + active2);
  });
});

<button id="btn1">Button1</button>
   <button id="btn2">Button2</button>

$btn1.click(function(){
    active1 = false;
    active2 = true;
    alert("after btn1 click: --> " + " active1: " + active1 + ", active2: " + active2);
  });