Thanks for the feedback @deraltetom.
The List Category Posts (LCP) developer, @picandocodigo, will need to work that into the LCP plugin. Jetpack does not control how LCP displays things. What Jetpack was doing at the beginning of this thread was actually a bug that has been resolved.
Here is a chunk of code that can be used as a 100% untested guide ;)
add_filter( 'jetpack_sharing_infinite_catch', '__return_false' );
// Do LCP display stuff
add_filter( 'jetpack_sharing_infinite_catch', '__return_true' );
If my guess is correct that should hide the sharing button output on the LCP lists but still show it on the main content.