There are very few themes that are incompatible with Product Customizer. If you're looking for a theme, we recommend themes from Out of the Sandbox. This team makes beautiful themes that work well with our apps.
Premium Plan Version
Our Premium Plan allows you to add pricing to your custom options. Since we use a hidden product to add this pricing to your cart, we need to be able to add a bit of code to your theme to hide this product. If you have questions about a custom theme, please reach out. We'll be happy to assess compatibility.
Most themes and carts work well with our Premium Plan. That said, some themes have optional drawer, popup, or other fancy carts. These carts do not work well with priced options. We typically recommend you disable these cart settings in favor of the default cart page. If you have questions about your theme's cart settings. Please send us a note, we'll be happy to work with you to make sure our app is properly installed in your theme.