There is not much more to elaborate. Can string theory say why electrons and protons have exactly opposite charge? And thus why hydrogen atoms are neutral? I guess that the answer is no, because nobody has yet deduced the standard model from strings.
The standard model does not answer the question: it just uses and requires the equality of charges for consistency reasons. (The "answers" to the similar question in the forum about the standard model show this clearly.) But standard model does not really explain the equality: why do two completely different particles have the same electric charge?
This said, does any other theory explain why the charges are equal?
Alternatively: why is the electromagnetic coupling of protons the same as the electromagnetic coupling of electrons?