Hello Wojciech,
Thank you for contacting WooCommerce support.
I understand that you would like to hide the shipping method on the cart and checkout page if the product’s shipping class cost is not applicable (N/A) or is set to 0.
To provide you with the best solution, I would like to confirm if you intend to hide just the shipping cost (which is zero). Or do you want to remove the Shipping Method which begs the question of how would customer complete the checkout process? Understanding this will help me tailor the guidance to your specific needs.
Meanwhile, it would be helpful to see a copy of your site’s System Status Report to ensure there are no underlying issues that might affect this change. Here’s how to get the report:
1. Go to your WordPress dashboard.
2. Navigate to WooCommerce > Status.
3. Select ‘Get system report’ and then click ‘Copy for support’.
After you’ve obtained the report, please paste it into a new Gist at https://gist.github.com. Once complete, simply paste the Gist link here in your reply.
I am here to help and look forward. ??
Best regards.