A resource manager as a organiser of day to day productivity has no place on an agile team. We know why they don't belong, it's in your question. They're trying to optimise things that oughtn't to be optimised. Their job is to figure out something else they can do with their skills that isn't counterproductive.

If their job is something more strategic and long term, like, for example in a staff-augmentation agency, making sure staff have new engagements to move on to after their current ones finish, then that still has a place. There exist activities that are outside of a development team, and that's one of them.

For that first type of "resource manager", if they are to continue being involved in the team on a day to day basis, they will have to look past their role and at how they contribute the team's outcome. Something needs to be arranged with the involvement of the team and their reporting manager, to best use their skills productively. Something ideally that doesn't undermine their career progression and leaves them with a role they enjoy and can do well. This is a hard problem and depends on the individual.