The layout issues are caused by the lack of the changes applied by Fluid Checkout on the WooCommerce AJAX calls that generate the HTML for the order review. The scripts and styles are being loaded, but the HTML is different than expected to apply the correct styles.
When deactivating/disabling Fluid Checkout globally with the Plugin Organizer, you also deactivate it for WC AJAX calls, which are needed to update the checkout state and refresh the checkout fragments.
Even if you activate Fluid Checkout only on the checkout page or via Plugin Filters, the plugin would be disabled for WC AJAX calls because it uses the homepage URL with query string parameters and the HTTP POST method.
You can use Plugin Filters to enable Fluid Checkout for the specific WC AJAX calls (see attachment). Although the wildcard char "*" does not work, so you'll have to add all the specific URLs -- luckily only two are needed (see below).
Also, keep in mind Fluid Checkout affects the following pages:
- Account > Addresses, changes to the address fields at checkout are also applied here.
The list of pages affected by Fluid Checkout might change in the future with the introduction of new features and with the launch of the PRO version.