The 'Gilded Age' of America mentioned in the submission title is this period of 1886-1896.
The whole review is a bit belaboured, or perhaps bogged down in detail, but tries to show how an analysis of this period can be used to understand the concept of equality today. The book apparently examines a number of different organisations that were founded in this time, such as the Grange, Women’s Christian Temperance Union, and the Knights of Labor. The claim is that these organisations were, at least in part, founded to try remove inequality but ended up leading to greater inequality.
> the national orientation of [these groups] led them to embrace a “white nationalist framework of sectional reconciliation.” The struggle against slavery cast a long shadow over the Gilded Age. The era’s radicals often viewed it as a model for their own activism. Yet because of their desire to organize nationally and to recruit members regardless of their Civil War loyalties, these groups played an important role in disseminating a view of that conflict in which slavery played only a minor part and Reconstruction was considered a disastrous mistake. This had dire consequences for black Americans and for an ideal of equality that transcended racial difference.
Their summary probably gets their point across most succinctly:
> Thanks to Occupy Wall Street, the presidential campaigns of Vermont Senator Bernie Sanders, the work of the French economist Thomas Piketty, and more generally the dysfunctionality of contemporary capitalism, equality—or the widespread lack thereof—again occupies a prominent place in political debate. Beyond the fate of the individual organizations it covers, Equality reminds us of a homegrown radical heritage that critics of today’s deeply unequal America can be inspired by and must improve upon. The ideal of equality remains as radical as it was in Jefferson’s day. But equality limited to some is not equality.