When did the us stop honoring dual citizenship?

US has not stopped Dual Citizenship. It was banned in the 19th century, however, due to changes in law, it was again revised in the 20th century. It is only allowed at considering certain circumstances. America considers many factors before issuing it to the individual irrespective of the country born. Individual's citizenship is based upon the parent's origin country. Suppose a child is born outside US, parents are US citizens, then the child will be given dual citizenship one from the country born and US citizenship based upon parents. Naturalization is also common nowadays for getting dual citizenship.