This is true for 3 reasons.
(1) Right now, they are perceived as an annoying, tax-eating minority in the UK. They have next to no representation in the UK government, since they constitute about 1.25% of the UK population.
In a united Ireland, where the tiny Protestant minority is treated quite well and is quite prosperous, they would become a 20% minority with substantial representation in the Dail. They would, ironically, have more control over their destiny than they would as part of the UK.
(2) The only reason for the IRA, that vicious pack of commie terrorist filth, to exist is the continued separation of NI from the rest of ireland.
In a united Ireland the Irish population, already disgusted by their behavior, would give up any residual support these criminals may still have. And if the Protestants negotiated an annexation directly with Dublin, demanding as a condition that the IRA be excluded from the negotiations, the IRA would be completely marginalized.
In a deterrorized, demilitarized NI the economy would skyrocket - and increased prosperity increases the resolve of the prosperous to maintain their prosperity.
That would require them to set aside ancient prejudices in favor of their own enlightened self-interest. Judging by the run of human history, the odds of that happening seem...slim ;)