apply_filters ( 'publicize_should_publicize_published_post', bool $should_publicize, WP_POST $post )

Notes

In the example below, we won’t publicize any post using the private tag:

/**
 * Do not trigger Publicize if the post uses the `private` tag.
 */
function jeherve_control_publicize( $should_publicize, $post ) {
	// Return early if we don't have a post yet (it hasn't been saved as a draft)
	if ( ! $post ) {
		return $should_publicize;
	}

	// Get list of tags for our post.
	$tags = wp_get_post_tags( $post->ID );

	// Loop though all tags, and return false if the tag's name is `private`
	foreach ( $tags as $tag ) {
		if ( 'private' == $tag->name ) {
			return false;
		}
	}

	return $should_publicize;
}
add_filter( 'publicize_should_publicize_published_post', 'jeherve_control_publicize', 10, 2 );

You can apply the same idea to ignore a specific category:

/**
 * Do not trigger Publicize if the post uses the `do-not-publicize` category.
 *
 * @param bool $should_publicize Should the post be publicized? Default to true.
 * @param WP_POST $post Current Post object.
 */
function jeherve_control_publicize_for_categories( $should_publicize, $post ) {
    // Return early if we don't have a post yet (it hasn't been saved as a draft)
    if ( ! $post ) {
        return $should_publicize;
    }
 
    // Get list of categories for our post.
	$categories = get_the_category( $post->ID );
	
	if ( is_array( $categories ) && ! empty( $categories ) ) {
		foreach( $categories as $category ) {
			if ( 'do-not-publicize' === $category->slug ) {
				return false;
			}
		}
	}
 
    return $should_publicize;
}
add_filter( 'publicize_should_publicize_published_post', 'jeherve_control_publicize_for_categories', 10, 2 );

You can apply the same idea to stop a specific user’s posts from being publicized:

/**
 * Do not trigger Publicize for a specific user.
 *
 * @param bool $should_publicize Should the post be publicized? Default to true.
 * @param WP_POST $post Current Post object.
 */
function ignore_specific_user_posts( $should_publicize, $post ) {
     
    // Assuming the user whose posts you want to ignore has the user id 2.	
    if ( get_current_user_id () === 2 ) {
        return false; 
    }
    
    return $should_publicize;
}
add_filter( 'publicize_should_publicize_published_post', 'ignore_specific_user_posts', 10, 2 );