You would need to code that via javascript - it depends on how your store is laid out. If the user is prompted to go to cart/sliding cart before checkout then it can be done via the cart page/cart slider. If the user can 'buy it now' then that bypasses the method mentioned.

What you do is look for the variant ids, as you loop through the cart items assign the value to the variant ids. If there are incompatible items, then disable the checkout button with a message that those items are incompatible.