Bazen

<form action="#" class="quiz__form_tourists">
  <button class="quiz__tourists-btn">
            Добавить ребёнка
        </button>
  <div class="years-old__inputs"></div>
</form>
<div class="quiz__block_years-old-wrap">
  <div class="years-old__title">
    Выберите возраст ребёнка
  </div>
  <div class="quiz__block_years-old">
    <button class="years-old__item years-old-1 box-shadow-hover">
                больше 2 лет
            </button>
  </div>
</div>

let formTourists = document.querySelector('.quiz__form_tourists');
  let btnTourists = document.querySelector('.quiz__tourists-btn');
  let yearsOldBlock = document.querySelector('.quiz__block_years-old-wrap');
  btnTourists.addEventListener('click', function(e) {
  	e.preventDefault();
    formTourists.style.display = 'none';
    yearsOldBlock.style.display = 'block';
  });

  let yearsOld1 = document.querySelector('.years-old-1');
  yearsOld1.addEventListener('click', function(e) {
  	e.preventDefault();
    formTourists.style.display = 'block';
    yearsOldBlock.style.display = 'none';
    let yearsInputs = document.querySelector('.years-old__inputs');
    let str = '<div class="years-input-wrap"><button class="years-input-remove">х</button><input type="text" class="years-input" placeholder="ребёнок до 2-х лет"></div>';
    yearsInputs.innerHTML += str;

    let inputRemove = document.querySelectorAll('.years-input-remove');
    
    for(let i = 0; i < inputRemove.length; i++){
    	inputRemove[i].addEventListener('click', function(e) {
      e.preventDefault();
      e.currentTarget.parentNode.remove();
    	});
    }
  });

вы забываете, что у вас больше чем 1 блоков "years-old__inputs". Поэтому используйте - querySelectorAll и добавляйте события в цикле.