Until 2001, America did not really care whether immigrants were Christian or Muslim. Until the recession of 2008, there really was not much of a backlash on immigrants from people already citizens of America. Whenever economic opportunities are not as robust as they used to be, there always is backlash against immigration. What is occurring in Brazil is not so much about demographics of immigrants, but about the fact that economic opportunities are not as robust as they used to be.
There are four strands to immigration issues. Availability of help to deserving immigrants with special skills — this is essence of the USA’s H1B visa program. Availability of help to those who never had opportunities for development of special skills in developing countries. This is essence of the USA’s visa lottery program. Third, management of inflows of immigrants, such that inflows are not so large they stifle opportunities of existing citizens, resulting in backlash to immigration. Fourth, encouragement of developing countries through grants, loans, technical assistance, all available through multilateral agencies or agencies of rich countries to invest in development of their countries.
The United States does a pretty good job of managing all four. Developing countries are well known for mismanaging the only one under their control, which is item four. Mismanagement has been so severe, the International Finance Corporation (IFC) sometimes ensures funds go directly to the private sector, do not pass through hands of developing country governments. Based on their actions then, even multilateral agencies are acknowledging developing countries mismanage resources that ought to be utilized for development of their countries. My point is, more needs to be done to induce developing countries to govern for the welfare of their people. If developing countries govern for the welfare of their people, demand for immigration to rich countries will decrease.
While items one to four must continue to be important to rich countries, if poor countries get poorer due to mismanagement in context of item four, is it feasible to expect rich countries to commensurately increase numbers of people they are willing to accept as immigrants? At any point in time, there always will be some maximum number of immigrants rich countries can successfully assimilate without disruption of existing economic equilibriums. It is exactly because of these economic realities that open borders, while aesthetically and intellectually appealing, are neither pragmatic nor workable.