I think it's a sign of a bad project manager if employees have to choose between their profession and the project. It's either that the project manager is not selling the project to the team members properly, or that he has not assigned team members to the project based on their expertise, but rather based on the project's needs.
I think if the project is already underway then it's already too late for a guaranteed corrective action, but there are some things that the project manager can do to rectify the situation, including:
- Shuffling tasks between team members so that each team member works on a task that is relevant to his expertise (this will only work if the project has more than enough resources matching the required skills set by the project).
- Clarifying the point behind the project. In other words, the project manager has to explain to the team members why the company is undertaking this project and how it will (positively) affect them when it's done.
- Constantly praising team members who are obviously not happy with their tasks, this will alleviate some of the pressure off their shoulders, and will somewhat clear the air.
- Getting the functional project manager on board. Quite often, team members look up to their functional manager and listen to everything that he says. If the functional manager can convince the team members that what they're doing is good for their expertise/career/profession, then you might have a motivated team again.
I couldn't understand your last question, could you please clarify it?