You got the preferred basis problem backward. It's one branch interpretations that have this problem, since the extant branch is absolute reality and its basis is absolute reality basis, hence the problem of privileged basis. In MWI all branches are relative and none is absolute reality, so their basis can't be thought of as absolute reality basis, branches and basis exist, but they are equal to others. This produces other criticism: universal wave function thus becomes spaghetti in which classical behavior is difficult to see when you look at it from outside, because the basis of classical behavior isn't privileged.