That's one of the arguments that the right uses to attack the idea of immigration, meaning immigration from Mexico. Although Mexico was in fact a one party state until fairly recently I don't think that the right wing commentators who make the assertion about Mexicans are actually basing their statements on an understanding of the history of the PRI, the Institutional Revolutionary Party, but are instead acting on a general racist impulse against Mexicans, as well as other Latino peoples. Yes, often times in the past when the question of dictatorships in Central and South America has been brought up in the public arena there's been either overt or covert suggestions that the reason they exist is because Latinos don't understand democracy. They don't say much about U.S. foreign policy.
But what's interesting is that this "don't understand democracy" argument, along with the idea that if there are enough immigrants that the U.S. will collapse into some sort of third world dictatorship, isn't new. In fact, it was used at the end of the 19th and the beginning of the 20th century as a justification to shut out immigrants from Southern and Eastern Europe, a campaign that actually succeeded after World War I. Why did they say that?
The argument was that Southern Europeans, principally Italians, came from a state without democracy, which wasn't true post-Italian unification in the 19th century, were racially inferior, and were Catholic, so would be under the sway of the pope and not able to make independent political decisions.
The argument against Eastern Europeans, actually Central Europeans, not people from Byelorussia, Ukraine, Romania, and Bulgaria, which are the true Eastern European countries, was that, unlike the Italians that at least had some sort of democratic state in the past, in the Renaissance and Rome, Eastern Europeans had never had anything like that, were essentially outside of history (an interesting concept coming from Americans who then more than now had no idea about geogaphy), spoke languages not even resembling English, and were Catholic as well.
The thought that people of Slavic descent could never understand democracy because of general backwardness and probable racial inferiority to Anglo-Saxons and Northwest Europeans.
Jewish people of Eastern European descent were even more of an unknown, outside of history, with classic anti-semitic fears being added to the mix.
In fact, although I only briefly looked at it, there was a book written pre-World War I, a classic "They're taking our jobs" book, named "The Slavic Invasion", dealing with mine workers from Slavic countries, which I'm assuming also meant Hungary and Baltic states even though they're not slavic.
Like I said, they eventually did pass a restrictive immigration bill, the Immigration Act of 1924, which was heartbreaking in its simplicity. Besides outlawing immigration entirely from many Asian countries, it instituted a 2% rule, something that demonstrates the absolute need to look at context to understand things. The 2% rule stated that only a number equal to 2% of the total number of people identifying as being of that ethnicity could immigrate to the United States. The census numbers used to compute this were from 1890 as well, which preceded the influx of Southern and Eastern European immigrants. ***on edit*** it seems that a total of 125,000 people per year were allowed in by the act, so the proportions gotten from the 2% calculation were then related to 125,000 people.
So because there was a large proportion of people identifying themselves, because they had recently emigrated or their fathers and mothers had recently emigrated, as Irish or German, in 1890, these ethnicities got preferential treatment in immigration while the others received official discrimination after 1924. Even though immigration had slackened off from Germany and Ireland.
Here's an example from Wiki:
"As an example of its effect, in the ten years following 1900 about 200,000 Italians immigrated every year. With the imposition of the 1924 quota, only 4,000 per year were allowed. At the same time, the annual quota for Germany was over 57,000. 86% of the 165,000 permitted entries were from the British Isles, France, Germany, and other Northern European countries."
Because North-Western Europeans, including the Irish here (who, despite all the Celtophilia surrounding them in the United States and their claimed history of oppression here, were thought to be better than Italians and Slavs and Jews), were thought to be able to understand democracy and be in harmony with the national character, while Southern Europeans and Eastern Europeans weren't.
It's funny how soon people forget these things and how, unfortunately, those who were abused in the past and are still at the bottom of the White ethnic hierarchy in the United States, like Italians, sometimes form part of the vanguard against immigration from Mexico today. Like people named "Tancredo". My intuition here is that Tancredo isn't an English name that you can find in the British census records going back centuries. Instead, if the Tancredos had tried to come over from Italy after 1924 there's a significant chance that they'd have been refused.
***Here is a chart put together by George Mason University showing the numbers of people allowed in after the act passed.
An example: 3,954 were allowed in from France per year, although French immigration to the United States was miniscule, while 3,845 Italians were let in every year, although 200,000 had been coming in yearly since 1900.