What you say may be true, but your mindset sounds a lot like the misguided thinking of (Southern Baptist leader)Richard Land on immigration. Land has bought into the myth that Hispanics are natural conservatives, and only vote Democrat because Republicans drive them away. They really want to vote Republican, but we’re just too mean! So he supports amnesty (’path to citizenship’ as he puts it...but that’s the same way all advocates of amnesty put it). He’s clueless. It apparently has escaped Land that it hasn’t been an embrace of liberalism by the American people that has resulted in abortion on demand and growing recognition of gay marriage; it has been a renegade judiciary imposing these things.
The decline of Christianity has of course contributed heavily to the decline of Western Civilization. It’s sad. The natives of Europe are largely ‘Christian’ in name only. The zeal that believers in Africa and Latin America have is admirable, but that doesn’t mean we will benefit by letting them come here. The idea that Western Civ can be saved by an influx of Third World people is just unfounded.
My father saw the thinned-out congregations of western Europe in 1945 and commented on them to me 15 years or so later, when I was old enough to receive such things. He told me that the only men he saw at Mass in France and Germany were gray-haired. None of the men of military or family age were in church. He didn't know why, but it doesn't take a mental giant to link the phenomenon to the rise of godless ideologies and scientism.
Not really talking about inviting them here, though I think missionaries should be welcome.