Как передать значение после JSON.parse?

да, все верно)

вот вроде рабочий вариант)) я бы сама не справилась))

var btnQuestion = $('.js-btnQuestion');
  var formRadioList = $('.form__radio-list');
  var popUpPoll = $('#js-popUpPoll');
  var namePoll = $('.js-namePoll');
  var btnQuestionAttr = JSON.parse(btnQuestion.attr('data-answer'));
  function createAnswer(answer){
    return '<label class="form__radio-label  form__radio-label--popUp">' +
        '<input type="radio" name="hobby" value="yes" class="form__radio-input" required data-true>' +
        '<span class="form__radio-mark"></span>' +
        '<span class="form__radio-sign">' + answer + '</span>' +
        '</label>'
  }
  btnQuestion.on('click', function () {
    namePoll.text(btnQuestion.attr('data-question'));
    popUpPoll.addClass('popUp--active');
    notices.removeClass('notices--active');
    var data = $(this).attr('data-answer');
    var answers = JSON.parse(data);

    $.each(answers, function(key, value){
      var answer = createAnswer(value);

      formRadioList.append(answer);
    })
  });