The membership button can be shown only on some specific products by following the below steps -:

Step 1: From Shopify Admin, go to the Online Store > Themes > Actions(Published Theme) > Edit Code(Published Theme).

Step 2: Open file product-template.liquid under Sections.

Step 3: Copy the below code and wrap it around the cart button element available in the file.

Step 4: Now, open the product in Shopify backend in which you need the membership button and copy its handle.

Step 5: Paste this copied product handle in the product-template.liquid file as mentioned in step 3.

Step 6: Now, copy the membership plan embed code and paste in the product-template.liquid file as mentioned in step 3.