Sinn Féin has not sat in parliament in any of its incarnations, starting with 1918, long. To do so would be to recognise the authority of the British state over Ireland, which we disagree with. For a few more practical justifications, SF MPs don't do NOTHING, they're working in the background to get concessions, deals made, etc. Just to cite an immediate local example, my MP for West Belfast recently was found to be in the top 10% of MPs in terms of work done for their constituents in a survey of all Westminster MPs despite having a literal absolute majority nearing 2/3rds of the vote and not taking their seat.
Acts of parliament historically don't benefit Ireland but work in the background does get results. The GFA had very little to do with parliament, for example. Abstentionism is not apathy, it's voted for by the people who wholly expect abstentionism. Westminster parliamentary democracy is also heavily flawed, with the popular vote and proportionate number of seats and actual representation being grossly inadequate. Look at the 2010 General Election in the North of Ireland for an example of that in action. Various Irish Unity supporters have sat in parliament and took their seats throughout history and their votes have made very little difference compared to any background work.
Granted, even everyone in SF can be frustrated sometimes by being unable to vote in Westminster elections purely out of pragmatism, but if anything it just reinforces how an utterly English-dominated parliament is barely even worth looking in the direction of thanks to the constantly reckless decisions of the English electorate sabotaging any chance for progress. By contrast, Stormont actually provides more proper proportional representation with its MLA system, almost as good as the Dail does in the South of Ireland.
And finally, there's the Oath of Allegiance, a no-go for various reasons, chief among which include history and pride. We don't believe in royalty~
