Before answering the above question, three egghead points are in order about facts, beliefs and public policy in general.
Egghead Point One: Few public policies come about through the following reasoned sequence: First, facts are brought to light; second, the facts lead to beliefs; third, the beliefs lead to public policy. An example of a reasoned sequence was the establishment of the TSA, whatever one may think of the agency. The sequence began with the fact that airliners were easily hijacked on 9/11. This led to the belief that airport security needed to be hardened, which in turn led to the public policy of establishing the TSA.
Egghead Point Two: For most public policy issues, beliefs come first; then, facts are cherry-picked or invented to support the beliefs, which in turn leads to public policy. An example was the Bush administration’s belief that Iraq was part of an Axis of Evil that needed to be defeated and transformed into a democracy. This in turn led to dubious casus belli for the public policy of invading the country and deposing Saddam Hussein and his Sunni regime.
Egghead Point Three: On other public policy issues, facts don’t matter at all; only values, ideology or philosophy matter. Abortion is an example. To simplify, the secular left thinks that a pregnant woman has rights, but an unborn fetus does not have rights. Conversely, the religious right thinks that a fetus is a human and has rights given by God. These are irreconcilable positions.
On a related note, loyalties also come into play, whether loyalties to a political party, tribe, race, socioeconomic class, or religion. As explained in the book, The Elephant in the Brain, absurdities are often used as a test of loyalty: the more absurd the position that a group takes, the more certain the group members are of each other’s loyalty. Some religions, for example, are full of absurdities. Likewise, political leaders often engage in absurdities, such as Trump pledging that Mexico will pay for the border wall or Hillary Clinton claiming that she lost the election because of Russian meddling. A group member who points out the absurdity risks being distrusted, or ostracized, or, in the case of religious fanaticism, persecuted.
Of course, self-interest can obviate all of the foregoing points. An unabashed free-marketer, for example, might be against government subsidies for private industry—until, that is, his hometown professional football team threatens to relocate unless taxpayers build a new stadium. When self-interest clashes with beliefs, values and facts—as it often does—the result is hypocrisy, cognitive dissonance, and intellectual contradictions.
All of these forces come together in the immigration debate.
First, what are the facts? Is immigration a net plus or net minus to the American economy and culture? Both sides have produced statistics down to a decimal point to make their respective cases.
Related question: Do all immigrants, regardless of race, ethnicity, nationality, culture, or education, have the same net plus or minus? Did my poor and poorly educated Italian immigrant grandparents contribute as much to society as the renown Italian physicist Enrico Fermi?
Is it even socially acceptable to ask this question in public? No, it is not; but much of the unspoken resistance to immigration is precisely because native-born Americans ask themselves such questions in private and come to the conclusion, correct or not, that unskilled and uneducated immigrants from certain countries cost more in welfare, education and policing than they contribute to society. They are not opposed to immigration per se, but to en masse immigration without admission standards.
Regarding cherry-picked facts, immigration proponents cite statistics showing that countries open to considerable multiracial, multiethnic, and multinational immigration have more innovation and better economic performance than those that are not as open, with all other variables being equal. But they conveniently overlook the success of such relatively homogenous countries as Japan, South Korea, and Taiwan, as well as the former city state of Hong Kong. At the same time, the proponents cite the benefits of diversity without mentioning diversity’s downsides—that is, the friction, mistrust, and sometimes bloodshed that has resulted throughout history where different races, religions and ethnicities have come into contact, especially at national borders.
Ideology and self-interest come into play in various ways. Libertarians tend to support open immigration, but only if there isn’t a welfare state to entice immigrants to become dependent on government. Democrats, on the other hand, want the welfare state to grow through immigration. Corporate Republicans just want the additional labor and customers that immigration brings, and blue-collar Republicans blame immigration for their declining income. Most of them cherry-pick facts to support their position, and the vast majority of them live amongst their own kind and have little firsthand experience or knowledge of life in the barrio, hood, ethnic enclave, mosque, temple, restaurant kitchen, slaughterhouse, or farm field.
Information abounds in the age of the internet, social media, and 24/7 news, but most of it remains second-hand information. It has been massaged, manipulated, and mangled by so-called experts with biases, hidden agendas, and cherry-picked facts.
Anyway, to answer the opening question, facts matter in the immigration debate, but not very much.