Here are some groups that would have approved of the Chinese Exclusion Act of 1882.
1) Nativist- Nativist are individuals who dislike immigrants and belief that the needs/wants of native born citizens should come first. This group often blames immigrants for taken jobs from American born citizens.
2) Laborers on the West Coast- In general, laborers or unskilled workers feared immigrant. This is because immigrants were often willing to work for less money than native citizens. If these people were restricted from getting into the country, this would help with job security.