Hardy, Nally Stand is correct to include partition in any definition of republicanism as as the complete independence for the country as a sovereign republic is at the core of Irish Republicanism. To their credit SF have never recognised the legitimacy of the border, whereas most other political party not only recognise it but have done little to nothing to try and end it.
Therefore the argument follows that by recognising the legitimacy of the border they are denying the legitimacy an Irish Republic ergo they cannot be Irish Republicans. They could be wishy washy republicans in a DeValera sort of way who are happy to replace the British monarch with the Pope and the landlords with bankers and builders, but not Irish Republicans in the mould of Tone, Emmet, Russell, McCrackan, Duffy, Davis, Meagher, Pearse, Connolly, Breen, O'Malley, O'Donnell, Connolly-O'Brien, McBride, Ryan etc...