Cause #1: Your Theme's AJAX Cart / Add-to-cart Script Does Not Support Line-item Properties
Pre-order Now's Mixed Cart Warning feature depends on the pre-order "cart label" being added to cart along with the pre-order product. Pre-order Now uses the pre-order cart label to determine whether a pre-order item is in the cart.
If you're not seeing a cart label in your shop when a pre-order product is added to cart, it's likely your theme's AJAX cart / add-to-cart script doesn't support Shopify's line-item property feature.
To resolve this, please contact your theme developer and ask them to add support for Shopify's "line-item property" feature to their AJAX cart / add-to-cart script.
Shopify has details on this feature here:
Once that's done, the Mixed Cart Warning feature should function properly.
Other apps use line-item properties to customize products as well, and so it's worth while having an AJAX cart / add to cart script that supports them.