The Immigration and Nationality Act of 1952
The McCarran Walter Act did break a barrier for Asian immigration. The Immigration and Nationality Act of 1952 brokedown the "Asiatic Barred Zone" which was a step in improving US relations with Asian nations. The "Asiatic Barred Zone" (otherwise known as the "Literacy Act") was another very discriminatory act.
People holding anti-communist rallies
It specifically targeted Asian areas and restricted them from entering the United States by forcing those over the age of 16 to pass a literacy test. This caused massive outrage.
The McCarran Walter Act specifically took away the Literacy Act to make it seem like this was not another xenophobic act, when in reality this continued to discriminate migrants with the fact that it alloted quotas based on race and not nationality.
So, although this act technically broke the barrier for Asians coming to the US by taking away the Literacy Act, it also created another barrier at the same time.