WordPress will automatically serialize the meta value and the function WordPress uses for serializing the value is maybe_serialize() which (unfortunately) will serialize the value even if it's already serialized like in your case.

So if the value is already serialized, then you would need to unserialize it before passing it to add_post_meta() to prevent the double serialization. Example using maybe_unserialize():

$value = 'a:2:{i:0;s:7:"noindex";i:1;s:8:"nofollow";}';
add_post_meta( get_the_ID(), 'robots', maybe_unserialize( $value ), true );

Why the content is not being respected

And it's not just add_post_meta(), but any functions like add_term_meta() and add_user_meta() that uses add_metadata().

And the reason why the value gets serialized again is because add_metadata() will automatically serialize the meta value using maybe_serialize() which (unfortunately) will serialize the value even if it's already serialized.

How to tackle the issue

In your case, if possible, pass an array instead of the serialized value/string:

// A non-scalar value will be automatically serialized by maybe_serialize().
$value = array( 'noindex', 'nofollow' );

add_post_meta( get_the_ID(), 'robots', $value, true );

However, if you retrieved/received the value from somewhere and you need to retain its exact format when saving, then — as you've already figured it out — you'll need to unserialize the value before passing it to add_post_meta() to prevent the double serialization.

But in WordPress, instead of using the native unserialize() function in PHP, I suggest you to use maybe_unserialize() instead:

$value = 'a:2:{i:0;s:7:"noindex";i:1;s:8:"nofollow";}';

// Unserialize the value and pass it to add_post_meta().
add_post_meta( get_the_ID(), 'robots', maybe_unserialize( $value ), true );