$postids = get_option('codeable_posts_field');This will give you a string of comma separated post ids (according to your code, and if the user follows the instructions).
array( $postids )will turn it into an array with that string as the only element. That won't work with is_single(), obviously, because is_single doesn't do any further splitting.
Here's how to turn that string into a proper array using preg_split. Replace
$postids = get_option('codeable_posts_field');with
$postids = preg_split("/\s*,\s*/", get_option('codeable_posts_field'));preg_split uses a regular expression to split a string into an array. I've added \s* before and after the comma so that it will work for 123,456 and also for 123, 456 or 123 , 456.
With $postids being an array, your check should work just fine. If it doesn't, try
var_export($postids);to see what $postids really contains.