add_action('init', 'save_landing_page_slider', 10, 2);
init is too early — if you look at the WordPress query overview on Codex,
init is (as of writing) the second step, whereas
is_ variables like
WP_Query::$is_page) that are used by conditional tags like
is_front_page() are only set in step 4, so instead of
init, you should use a later hook like
add_action( 'template_redirect', 'save_landing_page_slider' );
So in order for conditional tags to work properly, make sure to call them in the right hook or place.
Additionally, you should also understand when would
is_front_page() return true, e.g. when your homepage is set to a static Page, and that you’re on the homepage.