Csdrhrt

I think your requirements are just too restricting to find many examples.

There aren't that many cases of direct democracy in the first place, and "voted for the destruction of a minority" is a very high bar. There's a reason that people talk about the singularity of the Holocaust; there aren't very many places in time where people had 1) the desire and 2) the means to exterminate an entire people. A lot of discrimination is about exploitation, exclusion, or subjugation, not necessarily about annihilation.

I know of at least one example of violations of basic human rights in a direct democracy though. The people of Switzerland voted with 57% to forbid the building of minarets (which goes against the freedom of religion).

We can also see tyranny of the majority in non-direct democracies, such as the support of Germans for the NSDAP, the support of slavery and Jim Crow in the US, restrictions of basic human rights for LGBT people for much of the 20th century in western countries (proposition 8 would be an example of direct democracy), etc.

In 1879, California held a referendum on Chinese exclusion that passed the all-white electorate by a margin of 154,638 for to 883 against. It was later codified into law by elected representatives, both in the California Constitution as well as Federal Law.

In other words, 99.4 percent of the all-white California electorate voted to exclude all Chinese immigrants from the state forever. It was a remarkably unanimous show of nativist hostility toward a single immigrant group. Hatred of Chinese immigrants — the “indispensable enemy” — had become the one issue upon which white working-class Californians of all nationalities, religions, ethnicities, and political parties could agree.

In 1901, Alabama held a state-wide referendum calling for a constitutional convention with the express purpose to "establish white supremacy in this State". The resulting convention ultimately not only disenfranchised almost all African Americans in the state, but most poor white people also.

The second one may be a bit borderline, since it involved not only a massive amount of voter fraud in order to get passed, but the poor whites who were also disenfranchised were told that it was the only way to keep from being disenfranchised by the wealthy gentlemen who ran the convention. More information

In 1910, Okalahomans passed Oklahoma Initiative 10 that required proof of literacy in order to vote. There was a grandfather clause included allowing anyone to vote who was also entitlted to vote prior to January 1, 1866 ensuring that the qualification only applied to African Americans. The vote was 56% for to 44% against.

In 1963, the California Legislature passed the Rumford Fair Housing Act which attempted to prohibit racial discrimination by realtors and owners of apartment buildings built with public assistance. In response, the California Real Estate Association and other real estate groups helped place Proposition 14 on the November ballot, essentially nullifying the Rumford Act and ensuring a "right to discriminate" for housing sales and rentals, and was passed the same day Lyndon Johnson was elected president with almost 2/3 (65%) of the vote.

A direct example meeting even your strict criteria goes back to the time when the first critiques of democracy were made, in classical Athens. In 427 BC, the Athenian assembly decided, by simple vote, to massacre about a thousand prisoners of war. (The assembly reconsidered and changed from nearly unanimous to barely voting not to kill them all, which seems like both evidence of the power of a bloodthirsty majority and a pretty solid argument against the idea that people vote rationally.)

Frankly this is a pretty weak question (as tim answer's hints). Discrimination against minorities can happen in both representative and direct democracies. A better question would be if direct democracy really enables more discrimination than alternative (usually representative) democratic regimes. And it turns out there's an academic paper on tha (Gerber & Hug, 2002), finding in the negative.

In recent years, one of the most debated questions about direct legislation has concerned its effect
on minority rights. Recent theory suggests that these effects are both direct and indirect. Policy
advocates influence policy directly by passing or blocking new laws by initiative or referendum.
They influence policy indirectly when legislatures respond to the threat or use of direct
legislation. However, most empirical studies focus exclusively on outcomes at the ballot box and
so are limited to estimating direct effects. Theory also suggests that direct legislation institutions
mediate underlying voter preferences in specific ways. Using multivariate logistic regression
analysis, we compare the probability of having various minority protection and antidiscrimination laws in American states that do and do not allow direct legislation. We find that
permitting direct legislation has a minimal independent effect on minority rights policies. Rather,
its presence and use changes the mapping between voter preferences and outcomes. Thus,
depending on the nature of voter preferences, direct legislation institutions may either increase or
decrease minority protections.

But it's also worth noting that the topic is controversial, with prior research (not all US-based) having inconsistent conclusions. And even the US-based analyses are contradictory:

A number of recent studies have addressed the question of whether direct legislation
undermines minority rights [...].
Strikingly,
they arrive at very different conclusions. Gamble (1997), for example, concludes that in
American states and cities, direct legislation significantly curtails minority rights achieved
through the legislative process. Donovan and Bowler's (1998) results, based on analyses of state
level ballot measures on the civil rights of gays and lesbians, contradict some of Gamble's
findings. And Frey and Goette (1998) show that in Switzerland, comparatively few measures
restricting minority rights have passed in popular votes.

So the controversy lives on, I suppose.

I'll also point out that the conclusion depends on dataset and methodology. Gerber & Hug don't simply look at the direct legislation passed, but also consider indirect effects, i.e. in a state with a mixed (direct & representative) legislative regime, there's potentially a "threat of referendum" (my term) in which the population can overrule their representatives, which may change the legislative behavior of the latter, for better or for worse as far as minority rights go; it depends on the cultural inclination of the population.

A contemporary (2002) California study also found that if instead of narrowly focusing on the discriminating legislation, minority rights aren't all that affected by direct democracy:

Our analysis indicates that critics have overstated the detrimental effects of direct democracy. Confirming earlier critiques, we find that racial and ethnic minorities-and in particular Latinos-lose regularly on a small number of racially targeted propositions. However, these racially targeted propositions represent less than 5% of all ballot propositions. When we consider outcomes across all propositions, we find that the majority of Latino, Asian American, and African American voters were on the winning side of the vote.

On the other hand, a more recent (2007) review more narrowly focusing on LGBT rights found that direct democracy is detrimental to this group. A 2011 study came to the same conclusion regarding same-sex marriage.

A 2015 Swiss study found that direct democracy is more discriminatory over there when it comes to naturalization applications, particularly for minorities in the most xenophobic areas (but judicial review also plays a role):

We find that naturalization rates surged by 60% once politicians rather than citizens began deciding on naturalization applications. [...] the increase in naturalization rates caused by switching from direct to representative democracy is much stronger for more marginalized immigrant groups and in areas where voters are more xenophobic or where judicial review is more salient.

So I guess a tentative conclusion from all this is that direct democracy does enable more tyranny of the majority... in some contexts.

There is a modern example: in 1959 in Switzerland there was a referendum to give women the right to vote, it did not pass. In that occasion 67% of men voted to deny women the right to vote. To be fair, there were also women's organization that were against giving women the right to vote, but only men could vote. Women gained the right to vote in a second referendum held in 1971.

There are also many historical examples in medieval Italy involving Guelphs and Ghibellines. These were the main political factions in Italy during the High Middle Ages: one sided with the Pope, the other with the Holy Roman Emperor. The supporters of the losing side in a city were usually kicked out from the city itself. Not all of the cities were democracies, especially in the contemporary sense of the term, but many were.

Brexit is a very recent example. The referendum posed a binary question: remain in or leave the EU. When the decision to leave was made, the slim majority was able to strip away rights and freedoms from the minority.

In a representative democracy the views of both sides would be considered and a compromise found. In fact the terms of leaving the EU negotiated thus far represent only the views of the leave voters, failing to preserve any rights and freedoms for the rest.