There are likely several different ways to go about this, but I’ll share mine in case its helpful. What I like about Jared’s plugin is it brings CCB groups into the back end of WP and makes them available as a custom post type but doesnt do anything else. Its not bloated with a lot of other functionality that often limits you on how to present the group info on the front end. For that I turn to Toolset by wp-types. Toolset is a powerful plugin that basically allows you to do php without knowing php. It gives you a GUI interface to accomplish php coding. The Types plugin of the Toolset family creates CPTs, and the Views plugin makes it easy to display CPT content on the front end. In this case, wpccb is creating the CPT already so its doing the work of Types. Toolset “sees” this wpccb-created CPT which means you can use its data in Views.
So say you have a small groups page built with Divi, and on the page you want to recreate your own version (styled how you like) of CCB’s public group finder, with options to filter by group type, day, location, etc. You would create a View in Toolset that has both the search/filter fields and the search/filter results. Toolset allows you to drop this into your Divi page as a shortcode. Add a or change a group in CCB and its automatically displayed on the front end of your site.
There is a learning curve with Toolset but once you get the hang of it it is extremely powerful. Sermons, staff, events, etc can all be CPT’s created (Types) and displayed (Views) by Toolset.
wpccb lets you manage your groups info in CCB and Toolset Views lets you display this any way you like on the front end of your site. And if you change themes you can take this functionality with you, needing only to restyle it to match the new look.