A common way to do it is to initialize a boolean to true, if any field is empty or not valid then you assign false to this boolean. You return its value at the end of the validation function.

function check() {
  //no need to check === true here
  if (validation()) {
    document.getElementById('success').innerHTML =
      'Your account has been successfully created.';
  }
}

function validation() {
  let isValid = true;
  var fname = document.getElementById('fname').value;
  if (fname == '') {
    document.getElementById('fn').innerHTML = 'Please enter first name.';
    isValid = false;
  }
  var lname = document.getElementById('lname').value;
  if (lname == '') {
    document.getElementById('ln').innerHTML = 'Please enter last name.';
    isValid = false;
  }
  var birth = document.getElementById('birthdate').value;
  if (birth == '') {
    document.getElementById('bday').innerHTML = 'Please enter birthdate.';
    isValid = false;
  }
  var gender = document.getElementById('gender').value;
  if (gender == 'select') {
    document.getElementById('gndr').innerHTML = 'Please choose your gender.';
    isValid = false;
  }
  var username = document.getElementById('username').value;
  if (username == '') {
    document.getElementById('usr').innerHTML = 'Please enter username.';
    isValid = false;
  }
  var email = document.getElementById('email').value;
  if (email == '') {
    isValid = false;
  }
  var econf = document.getElementById('econf').value;
  if (econf == '') {
    document.getElementById('rt-eml').innerHTML = 'Please confirm your email.';
    isValid = false;
  }
  if (econf != email) {
    document.getElementById('rt-eml').innerHTML = 'Email did not match.';
    isValid = false;
  }
  var password = document.getElementById('password').value;
  if (password == '') {
    document.getElementById('pass').innerHTML = 'Please enter password.';
    isValid = false;
  }
  var pconf = document.getElementById('pconf').value;
  if (pconf == '') {
    document.getElementById('rt-pass').innerHTML =
      'Please confirm your password.';
    isValid = false;
  }
  if (pconf != password) {
    document.getElementById('rt-pass').innerHTML =
      'Password did not match. Try again. ';
    isValid = false;
  }
  return isValid;
}