Some product thumbnail templates has a call to action to add to cart or buy now. You need to be mindful of places in your template that include these. You do not want your gated items to be added to cart. Below is an example of how to hide these elements so that perc tagged products are not accessible.

<!-- PERC: BEGIN -->
{% liquid
  assign perc = false
  for tag in product.tags
    if tag contains 'perc:'
      assign perc = true
    endif
  endfor
%}
 <!-- PERCS ENGAGE: END -->

  {% if perc %}
	 <div >NFT exclusive product</div> <!--replace with whatever messaging you want -->
  {% else %}
   <!-- PERCS : DEFAULT VARIANT QUICK ADD: START -->
    <a data-variant="{{ variant.id }}" {% if variant.available %}href="/cart/add?id={{ variant.id }}"{% else %}href="{{ variant.url }}"{% endif %} class="{% unless variant.available %}unavailable{% else %}product-quick-add{% endunless %}">{% if product.has_only_default_variant %}One Size{% else %}{{ variant.option1 }}{% endif %}</a>
   <!-- PERCS : DEFAULT VARIANT QUICK ADD: END -->
  {% endif %}