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 [...].
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.