alt Hacker NewsMore specifically, that refers to the Northern Irish MPs from the Sinn Féin party who do not recognise the UK Crown as a lawful authority in NI, and hence, refuse to take an oath of allegiance to it. (They used to not recognise the Republic of Ireland as well, until the 1980s I think.)
I think they don't approve of the Crown as an authority even if they agree it's lawfully established?
It's more like an atheist refusing to swear an oath before God in a courtroom: even if you agree that the law says you must do so, you might still not want to give God that recognition. But worse, because God might also be the defendant and the judge in this case, and you have to swear not only that He might witness your testimony but also that you pledge allegiance to Him, so swearing that oath really impairs your ability to participate in a fair trial.