Direct democracy does not imply that everyone participate in every decision, merely that everyone has the potential to do so, with respect to constitutive matters. Prepetory committees would iron out most details.
Historical instances of politically soverign and stable direct democracies are exceedingly rare, and so it is difficult to say definitively that minorities would be treated better or worse than in representative democracy.
In the Athenian democracy minorities were inter alia excluded from political decision making - one had to be a male member of the ethnic majority to participate, there was no mechanism for obtaining citizenship other than blood.
However - in comparison to how other Greek cities treated them, metics (resident aliens) in Athens enjoyed far greater security and had codified rights.
To me this latter point is decisive in showing that the horizon of direct democracy is always towards greater inclusiveness. But one has to make up one's own mind on these matters.