In the last line sort calling without "ss" (SwapStrategy) - it is looks like always unstable:

module std.algorithm;

void schwartzSort(alias transform, alias less = "a < b",
        SwapStrategy ss = SwapStrategy.unstable, Range)(Range r)
    if (isRandomAccessRange!(Range) && hasLength!(Range))
{
    alias typeof(transform(r.front)) XformType;
    auto xform = new XformType[r.length];
    foreach (i, e; r)
    {
        xform[i] = transform(e);
    }
    auto z = zip(xform, r);
    alias typeof(z.front()) ProxyType;
    bool myLess(ProxyType a, ProxyType b)
    {
        return binaryFun!(less)(a.at!(0), b.at!(0));
    }
    sort!(myLess)(z);                               /// <-------------
}