It is your theme that is doing this. I also notice that you do not seem to have an archive.php template.

The search.php is calling the WordPress body_class() function. Using your functions.php, you can hook in to this and remove the blog and home classes. You can use force is_search to add the search body class.

As there is no ‘real’ page called ‘filter’, your code would then look to see if the page being loaded has the search body class, and if so, remove the blog and home classes:

add_action( 'body_class', 'my_custom_search_class');
function my_custom_search_class( $classes ) {
    // Remove 'blog' class
    if ((in_array('blog', $classes)) && (in_array('search', $classes))) {
        unset( $classes[array_search('blog', $classes)] );
    }

    // Remove 'home' class
    if ((in_array('home', $classes)) && (in_array('search', $classes))) {
        unset( $classes[array_search('home', $classes)] );
    }
    return $classes;
}

As long as that runs after our plugin adds the search class, all should work, otherwise it might need a low priority set.

Checking around, is_home and is_front_page will often return other pages IF the theme sees posts on the page, so you can get false hits. What is the code that you are using to determine of the slider is used?

What happens if you use is_home instead of is_front_page ?