check if post title in a custom post type exists in page

This is wrong (or at best very confusing).

$wp_posts = get_the_content('page'); // get content of pages.

Your note says “get content of pages” but what you’ve really done is passed a alternate more link text.

get_the_content( $more_link_text, $stripteaser )

But that is an unnecessary step as you have the post content passed into the callback as $content already.

Additionally, you are only setting $mv_title if ('movie_ronny' == get_post_type()){ but you are using it whether it is set or not. That is going to trigger Notices.

This should be more correct:

function get_post_type_title($content){
  if('movie_ronny' == get_post_type()){
    $mv_title = get_the_title(); //get title of movie post type
    $content = str_ireplace(
      $mv_title,
      '<a href="http://mylink.com">'.$mv_title.'</a>',
      $content
    ); //perform a search and replace.
  }
  return $content;
}
add_filter('the_content','get_post_type_title');