From blog of a genetic testing company called My Heritage DNA:

Hungary’s Secret: New Study by MyHeritage Reveals that Hungary Has the World’s Second Largest Percentage of Population with Jewish Ancestry

By Esther ·

August 14, 2019 A new study that we’ve conducted in conjunction with expert statistician and demographer Dr. Daniel Staetsky has uncovered that there are surprising numbers of people descended from Jewish ancestors in Hungary — far higher than previously estimated by demographers. Our analysis of a huge cohort of 1.8 million anonymized DNA tests — the first of its kind in Jewish demography research — has revealed that the country with the highest proportion of Ashkenazi Jewish ethnicity after Israel is Hungary, and not the United States as was previously believed. After Israel, the top countries in terms of significant Ashkenazi Jewish ethnicity were Hungary and Russia, followed by Argentina, South Africa, Ukraine, and then the USA.

So I imagine that they are counting people who are, say, 1/4th Jewish as Jewish in this. In the U.S., there aren’t yet a lot of people who are 1/4th Jewish, although there will be. When I look at list of old guys, like the Forbes 400 or the top political donors, most are either Jewish or gentile but not both. But, apparently, things are different in Hungary.

Update: They explain exactly what they are doing in terms of cut-offs below.

This shows that there is a significant number of people in Hungary who have a Jewish heritage background that they do not acknowledge, are not aware of, or that their ancestors intentionally repressed. MyHeritage collaborated with Dr. Daniel Staetsky, Director of the European Jewish Demography Unit at the Institute for Jewish Policy Research, who conceived the study…. Among the 100 countries included in the research, the country that stood out with the highest percentage of Ashkenazi Jewish ethnicity outside of Israel was Hungary. 7.6% of the 4,981 people living in Hungary who took the MyHeritage DNA test were found to have 25% or more Ashkenazi Jewish ethnicity (equivalent to having at least one grandparent who is fully Ashkenazi Jewish). This is a significantly higher percentage than the 3.5% observed in DNA test-takers living in the USA and the 3.0% in Canada.

Keep in mind that people who are part Jewish might be more inclined to pay for a DNA test to find out than a random person.

Hungary’s lead grows further at lower thresholds for Ashkenazi Jewish ethnicity. 12.5% of the people tested in Hungary have 10% or more Ashkenazi Jewish ethnicity, compared to only 4.7% of people in the USA and 4.0% in Canada. Meanwhile, 4.2% of people tested in Hungary have 50% or more Ashkenazi Jewish ethnicity (equivalent to having at least one parent who is fully Jewish), compared to 2.3% in the USA. … Dr. Staetsky suggests accounting for a degree of selectivity of MyHeritage users. Since commercial genetic testing is an activity where the most educated and well-to-do classes of a society will be over-represented, he accounted for such selectivity, estimating the number of people with 50% or more Ashkenazi Jewish ethnicity in Hungary as 130,000. This is significantly higher than some recent estimates. Official statistics set the number of Jews in Hungary at only 10,965, according to the 2013 national census. Alternative estimates, such as the estimate produced by Professor Sergio DellaPergola, show that the number of people in Hungary who self-identify as Jews — for example, when asked in a survey — comes to 47,500 people or 0.49% of the population. Larger estimates of the population with Jewish ancestry in Hungary, produced by Professor Andras Kovacs, give a range of 73,000 to 138,000 people with at least one Jewish parent. Thus, the estimate based on MyHeritage data aligns well with the high end of some demographic estimates, lending credibility to both the traditional demographic methods and to the novel estimates based on genetic testing. Ashkenazi Jews throughout the past centuries have lived in isolated communities that developed unique genetic signatures. … Previous studies have found Ashkenazi Jews to be a clear, homogeneous genetic group. … Jews have a long history in Hungary, with Jewish officials having served the king during the early 13th-century reign of Andrew II. By the early 20th century, the Jewish community constituted 5% of Hungary’s total population (comparable to MyHeritage’s findings) and Jews comprised 23% of the population of the capital, Budapest. Seven of the thirteen Nobel prize winners born in Hungary are Jewish. However, by 1941, over 17% of Budapest’s Jews were Roman Catholic converts, following coordinated pressure across Europe that began with the Spanish Inquisition in the late 15th century. Like many ethnic minorities in the Austro-Hungarian Empire, Hungary’s Jews had rapidly assimilated in the decades preceding the Holocaust. In the Holocaust, about 560,000 of Hungary’s Jews were murdered. The trauma of the Holocaust and the subsequent communist rule led to portions of the Jewish community either being completely unaware of their Jewish identity or discouraged from divulging it. … In Russia, the study revealed results similar to those in Hungary, with many more people having Jewish ethnicity than expected by demographers. 7.5% of the 5,266 DNA test-takers living in Russia had Ashkenazi Jewish ethnicity of 25% or more, making it the country with the third-largest percentage of Jewish ethnicity in the world, after Israel and Hungary. … When setting the threshold of Ashkenazi Jewish ethnicity at 50% or more, the percentage in Russia drops to 3.1%, compared to 4.2% in Hungary. This indicates that in Russia, people who were ethnically Jewish tended to marry non-Jewish people at a greater frequency than in Hungary, which means that Jewish ethnicity in Russia is dissolving at a higher rate than in Hungary.

Here in the San Fernando Valley, there are now a whole bunch of people who are kind of Russian and kind of Jewish. Maybe they were born in the Soviet Union, qualified as Jewish enough to move to Israel, then bounced to L.A.

You don’t hear about them a lot, even though they congregate at the heart of the entertainment industry in places like West Hollywood and The Valley. One reason is because conventional American-born Jews are lately heavily into Russophobia, seeing Putin as the neo-Czar, so the existence of a lot of kind of Jewish Russians and kind of Russian Jews is disconcerting for the predominant worldview in which Russians are seen as dangerous anti-Semites.

Razib Khan points to intermarriage as early as 1780 for the diffusion of Jewish genes in Hungary:

A massive wave of demographic expansion occurred among Ashkenazi Jews after 1500. In the 18th-century Jewish fertility was far greater than gentile fertility in Poland. This resulted in an increase in the Jewish proportion over time, but likely also assimilation of some Jews into Christian society. The “Jewish Enlightenment”, spanning the 100 years between 1780 and 1880, was also a period when massive defections occurred from the more integrated elements of the Central European Jewry. Moses Mendelssohn’s last male descendant to practice Judaism died in 1871, after one century of assimilation and conversion.

Budapest was famous for smart Jews (e.g., John von Neumann), which I suspect correlates with early openness to intermarriage.