I’m using Roots Bedrock + Sage 9 Beta 3. I’ve created a custom post of type lp that I want to set as my homepage. Here is the code I’m using:

function cptui_register_my_cpts_lp() {

    /**
     * Post Type: Landing Pages.
     */

    $labels = array(
        "name"          => __( 'Landing Pages', 'sage' ),
        "singular_name" => __( 'Landing Page', 'sage' ),
    );

    $args = array(
        "label"               => __( 'Landing Pages', 'sage' ),
        "labels"              => $labels,
        "description"         => "Pages without menus and/or totally custom layouts.",
        "public"              => true,
        "publicly_queryable"  => true,
        "show_ui"             => true,
        "show_in_rest"        => false,
        "rest_base"           => "",
        "has_archive"         => false,
        "show_in_menu"        => true,
        "exclude_from_search" => true,
        "capability_type"     => "post",
        "map_meta_cap"        => true,
        "hierarchical"        => false,
        "rewrite"             => [ "slug" => "lp", "with_front" => true ],
        "query_var"           => true,
        "menu_icon"           => "dashicons-welcome-widgets-menus",
        "supports"            => [ "title", "thumbnail", "excerpt" ],
    );

    register_post_type( "lp", $args );

}

add_action( 'init', 'cptui_register_my_cpts_lp' );

I’ve installed mpress-custom-front-page but it doesn’t seem to see my landing page.

So, with some digging, I noticed that it uses get_posts() to get posts with post_type="any".

The query it sends is so:

$queried_post = get_posts([
  'posts_per_page' => - 1,
  'orderby'        => 'title',
  'order'          => 'ASC',
  'post_type'      => 'any',
  'post_status'    => 'publish',
]);

This query returns all of the posts except my custom post types:

If I redo this exact query, but set post_type to 'lp' then I get my post, no problem:

Why would any not find my custom post type?

Because when registering your post type you have 'exclude_from_search' => true

get_posts() is just passing that to WP_Query. In the parameter definitions for WP_Query it states:

‘any’ – retrieves any type except revisions and types with ‘exclude_from_search’ set to true.