Last updated date function

You can check for your “home page” at the start of your function by using is_home() and/or is_front_page() and just return original content without date. See is_home vs is_front_page

function wpb_last_updated_date( $content ) {
  if ( is_home() || is_front_page() ) return $content; //homepage return content without date

  // your original function code

}

Alterantively you could embes your add_filter in an if statement