The Citadel Concordance says:
The sept of Lordsport was also destroyed by Robert Baratheon's forces, but unlike the stronghold of the Botleys and the village it was never rebuilt
This squarely lays the blame on Robert's forces (Which is curious, given that the bulk of the Royal Forces were followers of the Seven, but that's not the point of the question.)
The ASOIAF wiki makes no mention of the forces responsible:
During Greyjoy's Rebellion, Lordsport and its timber and wattle keep were the first places on Pyke to fall when King Robert I Baratheon and his forces landed on the island. The keep and the village were razed and the sept was burned to the ground.
The cited chapter itself does not make any mention of who destroyed the sept:
When last he’d seen Lordsport, it had been a smoking wasteland, the skeletons of burnt longships and smashed galleys littering the stony shore like the bones of dead leviathans, the houses no more than broken walls and cold ashes. After ten years, few traces of the war remained. The smallfolk had built new hovels with the stones of the old, and cut fresh sod for their roofs. A new inn had risen beside the landing, twice the size of the old one, with a lower story of cut stone and two upper stories of timber. The sept beyond had never been rebuilt, though; only a seven-sided foundation remained where it had stood. Robert Baratheon’s fury had soured the ironmen’s taste for the new gods, it would seem.
ACOK - Theon I
This only mentions that the town was burnt and the people rebuilt it, with the exception of the Sept. So why does the Citadel blame Robert's forces in no ambiguous terms? What proof do they have that it was Robert? Given that the Faith was barely tolerated in the Isles and Balon only fanned the religious/ethnic tensions before and after the rebellion, it is entirely possible that the Ironborn may have done it themselves, to send a message of sorts that there was no place for New gods on the Isles any more.
Who actually burnt down the sept?