Use Gravatar through a WebP-friendly endpoint.

General usage

Change the hostname from www.gravatar.com to gravatar.webp.se. The /avatar/:hash path stays the same.

WordPress

Add the following filter to your active theme's functions.php. It normalizes the standard Gravatar hostnames and then routes the generated avatar URL through the public service.

function use_webp_public_service($avatar) {
    $avatar = str_replace(
        array("www.gravatar.com", "0.gravatar.com", "1.gravatar.com", "2.gravatar.com"),
        "secure.gravatar.com",
        $avatar
    );
    $avatar = str_replace(
        "https://secure.gravatar.com",
        "https://gravatar.webp.se",
        $avatar
    );
    return $avatar;
}
add_filter("get_avatar", "use_webp_public_service");

Theme files may be replaced during a theme update. If your site uses a child theme or a snippets plugin, place the filter there instead.