Remove categories from post edit page, but keep in sidebar?

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You can hide them in the Screen Options dropdown (which is a per-user basis) if that’s what you’re looking for:

screen options dropdown

You could also remove the metaboxes with remove_meta_box seen here: https://codex.wordpress.org/Function_Reference/remove_meta_box

So depending on what the HTML ID of that custom box is, you could add a function. Let’s say Client Types is client-types, then the following should do the trick:

function remove_post_custom_fields() {
  remove_meta_box( 'client-types' , 'post' , 'normal' ); 
}
add_action( 'admin_menu' , 'remove_post_custom_fields' );

That would hide it for all users in the Post screen.