function compareStatus() {
  if(valueTruebutton === statusRandomrapper) {
    alert("Both status are true");
  } else {
    alert("Nah, those status are different");
  }
}

var valueTruebutton = document.getElementById("truebutton").value;

var rapperA = {firstName:"A$AP Rocky", image:"test.jpg", clip:"test.com", status:"true", smallthumbnail: "test.png"};

<button id="truebutton" onclick="compareStatusTrueButton()" style="background-color: #4BCC92; border: none; font-size: 2em;" value="true">True</button>

console.log("randomRapper.name:" + randomRapper.firstName + ", randomRapper.status: " +  randomRapper.status + " valueTruebutton: " +  valueTruebutton + " valueFalsebutton: " +  valueFalsebutton )