There are very few themes that are incompatible with Product Personalizer.
Most themes and cart pages will work just fine with the the app; however, some themes have the ability to use “drawer”-style carts in your store. These drawer carts will not work with products whose options have costs associated with them or image upload option; drawer carts to do not refresh the page when updating, and thus will not upload file (as shopify does not support) & apply pricing changes when product quantities are updated. (This could cause incorrect order totals with personalizations.)
Please view our document on drawer carts to see which themes have these cart types, and how to disable it.