Do PBP identity as nationalists or as "who care"?
They officially designate as "others". Their voters, on the other hand, would overwhelmingly identify as nationalist. Carroll's second preferences in West Belfast went:
SF: 1546.16
SDLP: 760.76
Green: 378.84
Alliance: 136.40
UUP: 14.96
DUP: 14.52
The SWP, whose front organisation PBP is, was "critically supportive" of the Provisionals during the conflict. The SP, on the other hand, whose front organisation is "Cross Community Labour Alternative", is in favour of a Socialist Federation of Ireland within a Socialist Federation of The British Isles, not that it's likely to bring up that particular ideological quirk on the doorsteps of either Jobstown or the Lisburn Road.
They just got a second seat.