[i.h]

They can.

maybe there's some nuance I'm missing, but how does it differ to other multi-union workplaces where they don't do that? Isn't a "director" a different job role? Unless BECTU are also in dispute & have given notice that they would be striking on the same day, I'm not sure they can (legally).

I know of one company where Prospect/BECTU had to make clear that it was not involved and so its members should continue to work as normal, the other union's picket line is not aimed at them, but should refuse to cover for those who are on strike & the union would help back them up on that.