No, it is not morally wrong. In fact, it is morally wrong not to suspend all immigration.
Our forefathers fought for their independence from the rest of the world so that they and their children could live in peace, in a nation which reflected their own values and traditions. They anticipated that their great, great, great, great, great, great grandchildren, and their descendants in perpetuity, would inherit this country, and that they would be guaranteed rights to life, liberty, and pursuit of private property so long as they found themselves within its borders. They anticipated that population growth would derive predominantly from their own families, and the families of their civic-minded countrymen, and not from foreign journeymen seeking wealth. They designed the government so that it would reflect the will of citizens, and so that power could not be easily usurped by opportunistic outsiders. Indeed, this may be said of almost every nation on Earth. Loyalty to one's own, to the exclusion of others, is the essence of nationhood.
Nevertheless, our government (speaking specifically of the USA) had one fatal flaw: it did not clearly outlaw birthright citizenship for immigrants merely present on our soil. Over time, it allowed populations with zero appreciation for this country's freedoms, and zero affinity for its founders, to propagate and congregate in large masses. These groups now wield political power, though they have little historical connection to the country itself. Naturally, as minorities, they are aggrieved. Because their ancestors did not build this country, they perceive this country's history as that of "dead white men." Thus, our history, customs, traditions, holidays, etc. – all of it is easily discarded, as it is utterly meaningless to them. Because their ancestors fled, rather than fought for their homelands, they perceive firearms and offensive speech as inherently evil, rather than as deterrents against evil. Because their ancestors came here expecting personal wealth, they value their citizenship only so far as it guarantees them personal wealth. For many, their concept of government is purely transactional: "what can the government give me?" In this regard, their relationship to government is akin to that of a child seeking an allowance. If they receive no allowance, they will throw a tantrum. They will never feel at home in this country, no matter how many time-honored institutions they destroy. They will always perceive persecution from the majority, even as their own numbers grow, and as the majority shrinks to a mere plurality.
In short, we will never be united. By leaving open the floodgates of the third-world, we have doomed our descendants to fight yet another bloody war for independence. There is definitely something "morally wrong" with that.