Both western europeans and latin american people could immigrate "freely" under that immigration act. The act was intended as a mean to limit the immigration of people whose ancestry was "non white", while increasing the number of "white" inmigrants to guarantee a more homogeneous population in the US. The first group of people was allowed to immigrate because many people living in the US came from the british islands, and in the case of latin american people, since they were a mixture of european and native american parents, they were considered as "white", too. People not allowed to immigrate under this act: asians and east europeans.
The western Church claimed authority over the Eastern Church because the pope believed he had power over both Churches.