Would there be any adverse effects on the world if people took note of this, causing the distribution of birthdays to change so that there was a significant spike during the May-July low-risk period?
That's a very important point. The effect (if it were to be proved) could be reversed in the southern hemisphere, and completely absent in non-city environments. I'm plucking those hypotheses out of thin air, but it seems obvious that the risk goes up because of some underlying reason.
Perhaps being born in New York in October increases the chance that you'll spend most of your first few months of life in a damp-infested flat without much natural light. Perhaps it's because of increased stressed levels at school associated with being one of the oldest in your peer group.
Without knowing the underlying causes, this is just an interesting tidbit.