Dominicans give citizenship to anyone whose parents are born in the Dominican Republic.
As one gets off the plane there is usually a both before elections, asking all Dominicans to get their cedulas in order to vote. They have voting booths for the Dominican elections in a lot of cities in the US.
I think that you would start losing rights if your parents are born here but you never get a cedula or passport and then wanted your child to become Dominican.
But for now, your child is entitled to dual citizenship as long as you were born here. Just like an American can confer US citizenship on their children no matter where they were born.
The woman at the consulate is wrong.
Renunciation Process Step-by-Step | Renunciation of U.S. Citizenship: A Web Guide
you have to go through a big deal to renounce US citizenship... probably because the IRS can tap you for tax no matter where you live.. unlike other countries.
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Thank you for your thoughtful responses, I will followup with them.