[MatrixMedia]

to exclude some categories I have tried this:

function exclude_category_slugs_from_activity_stream( $new_status, $old_status, $post ) {

	// Only record published posts
	if ( 'publish' !== $new_status ) {
		return;
	}

	// Don't record edits (publish -> publish)
	if ( 'publish' === $old_status ) {
		return;
	}

	// add in any categories to exclue from activity stream, separated by commas, no spaces
	$category_slugs_to_exclude = "news,new,News,service,Service";

	// create the array that contains the category ids to exclude
	$ids_to_exclude = array();
	// create new array by splitting category slugs by comma
	$category_slug_array = split( ",", $category_slugs_to_exclude );
	// iterate over category_slug_array
	foreach ( $category_slug_array as $category ) {
		// get the category id based on the slug
		$idObj = get_category_by_slug( $category );
		$id = $idObj->term_id;
		// push the category id onto the exclude array
		array_push ( $ids_to_exclude, $id );
	}

	// get the post's categories
	$categories = get_the_category( $post->ID );
	$in = false;

	// check if the post has any categories, do nothing if not
	if( count($categories) > 0 ) {
		// iterate over categories
		foreach ( $categories as $category ) {
			// check if any excluded category exists within post's categories
			if( in_array( $category->cat_ID, $ids_to_exclude) )
				$in = true;
		}
	}

	// Don't record posts from filtered categories
	if( $in )
		return;

	return bp_activity_post_type_publish( $post->ID, $post );
}

add_action( 'bp_init', 'bp_blogs_catch_filtered_published_post' );

function bp_blogs_catch_filtered_published_post() {
	if ( bp_is_active( 'blogs' ) ) {
		remove_action( 'transition_post_status', 'bp_activity_catch_transition_post_type_status', 10 );
		add_action( 'transition_post_status', 'exclude_category_slugs_from_activity_stream', 10, 3 );
	}
}

I found here: https://premium.wpmudev.org/forums/topic/exclude-auto-blog-posts-from-buddypress-activity-stream

of course I changed the deprecated functions:
bp_blogs_record_post -> bp_activity_post_type_publish
bp_blogs_catch_transition_post_status -> bp_activity_catch_transition_post_type_status

but nothing … not working … HELP!!!

[MatrixMedia]

sorry, I have not explained well, the second point, I Repeat:

I also tried to customize the Post Types default ‘post’, following this guide: https://codex.buddypress.org/plugindev/post-types-activities/

this is my function:

add_post_type_support( 'post', 'buddypress-activity' );
function customize_page_tracking_args() {
    // Check if the Activity component is active before using it.
    if ( ! bp_is_active( 'activity' ) ) {
        return;
    }
    bp_activity_set_post_type_tracking_args( 'post', array(
        'component_id'             => buddypress()->blogs->id,
        'action_id'                => 'new_blog_post', // or 'new_post'
        'bp_activity_admin_filter' => __( 'Published a new post', 'emt-buddypress' ),
        'bp_activity_front_filter' => __( 'Posts', 'emt-buddypress' ),
        'contexts'                 => array( 'activity', 'member' ),
        'activity_comment'         => true,
        'bp_activity_new_post'     => __( '%1$s shared a new <a href="%2$s">post</a>', 'emt-textbuddypress' ),
        'bp_activity_new_post_ms'  => __( '%1$s sahred a new <a href="%2$s">post</a>, on the site %3$s', 'emt-textbuddypress' ),
        'position'                 => 100,
    ) );
}
add_action( 'bp_init', 'customize_page_tracking_args' );

but when I publish a post on activity stream, is not displayed. If I remove the function or use a new custom_post_type, in this function, it works.