The Naturalization Act of 1790 (http://rs6.loc.gov/cgi-bin/ampage?collId=llsl&fileName=001/l...) limited gaining US citizenship to "free white"s, but said nothing about entry of others.

With some exceptions (such as the Chinese Exclusion Act), national/ethnic-based restrictions for entry into the US did not come about until the Emergency Quota Act of 1921, the purpose of which was to maintain the US's ethnic balance as of the 1910 census. It had many, many exceptions (such as the skilled of any race) and exemptions (all of Latin America, for example). None of the above changed the Ellis Island restrictions I mentioned: No proof of financial support (whether of oneself of from another), no entry.