The answer to this has got to be Haiti.
Of the countries that you list here, Haiti became a republic before any except the United States. Haiti became independent in 1804. The other countries did not become independent until later in the 1800s or even until the 1900s, in the case of Jamaica.
The United States clearly did not grant equality to all of its citizens until after the US Civil War in the 1860s, so that cannot be the answer either. In Haiti, there was no slavery after independence. By 1825, there were no laws against interracial marriage (that took until 1965 to happen in the US).