Content Templates modify the content when called from the WordPress’ built-in the_content function. Some themes do not use the_content function, but define their own function. In this case, Content Templates are not applied to selected posts on the front-end.

To solve this, you can enter the name of the function your theme uses on the Toolset->Settings page, under the Front-end Content tab. You can find the appropriate field in Theme support for Content Templates section.

Theme Support For Content Templates - Function Name Field
Theme Support For Content Templates – Function Name Field

You should never add the following generic functions to this section: require, require_once, include, include_once, locate_template, load_template, apply_filters, and call_user_func_array. Adding them will result in infinite loops when rendering a page with a Content Template, or pages that feature WYSIWYG fields. If after running the debug tool you get some of these functions, then your theme needs adjustment to work properly with Content Templates. You need to edit your theme files to provide a proper function that displays the content. In this case, it would be best to contact our support for help with debugging and instructions.

If you don’t know the name of your theme’s function, check the Enable theme support debugging option and click Save.

Theme Support For Content Templates - Enable Debugging
Theme Support For Content Templates – Enable Debugging

Now, go to a page that should be displayed using a Content Template and copy the call function name that Views displays. Go back to the Front-end Content tab in Toolset Settings and paste the name of the function into the Theme support for Content Templates section.

Theme Support For Content Templates - Enter The Name Of The Theme's Custom Function
Theme Support For Content Templates – Enter The Name Of The Theme’s Custom Function