You're wrong about this ... my grandfather immigrated to the U.S. in 1902 through Ellis Island - there were laws, rules, procedures, and policy in place, including a health exam and quarantine.
The 1920's immigration rule modifications dealt with the numbers allowed in, and established the nationality quotas that remained in place until the Ted Kennedy revisions in 1965.
1917 (to be exact) saw the passage of "Asia Barred Zone". Further laws in the 1920s, for example the Johnson-Reed Act of 1924, also known as the Permanent National Origins Quota Act, began a quota system that lasted for 40 years.
This act, combined with standards regarding citizenship, whether statutory or precedental, clearly established that Asians were not welcome, and neither was anyone else who might look Asian.
Classically the national origins quota system has been taught in public schools as justified by the influx of Italian and Greek immigrants who sought to come to America "only to make money" and who "refused to assimilate".
I've always thought it remarkable that even before the economic dislocations that began in 1929, our Solons in Congress had in 1924 the wisdom and foresignt to see that Greeks and Italians might decide to return home rather than starve to death in breadlines in the Great Depression nearly a decade later.
I think the restrictions you are referring to regarding your grandfather were those barring idiots, syphilitics, anarchists, polygamists and folks with TB. Guess he passed the tests.