I chose A. At first, 'it' definitely refers to 'schedule' because 'he' refers to 'the manager'. it's impossible to use two pronouns to refer to two things in one question. Second, it's not necessary to use 'would have to' at all. And 'must do' is more simple than 'would have to'. The above two reasons can exclude answer D "what everyone is assigned' can be regarded as a fact. I think it's better than 'was' because probably those employees won't start their work until both the manager and labor know the schedule. 'was assigned' implies a fact that maybe everyone has done what they were assigned.
i also vaguely remember from one of the grammar books that the difference between the two is:
must -- is more objective, emphasizing a person's belief/opinion/will have to -- has the implicit meaning that 'no matter you like it or not, you've got to do it'. more subjective.
that explains why 'it must be posted' is used. since the 1st part says 'althought...', implying the 'manager's unwillingness to accept 'the change of schedule'. thus, the idea that the schedule must be posted is more of the manager's personal opinion (as a means of retaliation).