Definitely second-class status. As WOIAF points out: “Just as Arlan III Durrandon had done three centuries earlier, Harwyn claimed the riverlands for himself. Those riverlords who had fought beside him had done naught but exchange one master for another…and their new master was harsher, crueler, and more exacting than the old one.”
The Ironborn taxed the Riverlands mercilessly to pay for the Hoare’s wars against the Westerlands, the Stormlands, and the Vale, demanded tribute from the local lords on top of it, took Riverlander women as salt-wives, and you’d better bet Riverlanders were used as cannon-fodder thrown at the Bloody Gate, and then there’s Harrenhal, for which “Harren the Black had driven thousands to their deaths in the building of his great castle of Harrenhal, plundering the riverlands for materials and beggaring lords and smallfolk alike with his appetite for gold.”
So basically the best the Riverlords could hope for is to be treated as local quislings for a gang of brutal tyrants.
And just to be clear, by this point in the history of the Iron Islands, the whole “all captains equal in the Kingsmoot” thing doesn’t exist. There hadn’t been a kingsmoot for thousands of years, ever since Urron Redhand, and the Hoare kings ruled by right of blood.