Assuming the original births were Protestant (specifically CoI), I would suppose the primary reason was economic, somewhat comparable to how so many converted Islam, after the Islamic conquest.
At the extreme end, (with what level of enforcement I don't know) I believe, at one time, by law, the Catholics were not supposed to even work the land on the larger estates in the Ulster Plantation, let alone own land. Now, I'm not sure whether this applied to Antrim or not, but perhaps they saw the writing on the wall anyway.
It would have been pretty hard to be a Catholic in Ulster, I think. Under Cromwell, Catholic churches were destroyed or converted all over Ireland. Mass was usually held outside and in secret. They were still hunting priests at least as late as 1700.
I wouldn't suppose that your family would be on the rolls. I think they involved a bit of travelling, and likely many families converted beforehand.
My understanding is that there was a lot of unofficial discrimination, especially in Ulster, for a long time, even after the Penal Laws were lifted. Ulster was sort of economically depressed compared to England, and people looked out for their own, in terms of resources, so it isn't inconceivable that an open job would be filled preferentially by a Protestant.
