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. It's counterproductive.
It could be possible that this "resource manager" is more strategic role than it sounds. For instance, at a staff-augmentation agency, there are people making sure that developers have new engagements to move on to after their current ones finish. That's a useful job, but it doesn't involve day to day meddling in a team. And if that's happening, the team need to object to it and escalate their concerns.
But, if the "resource manager" is a role that exists day to day in the team that we have a problem. That person will have to look past their role and at how they contribute the team's outcome. Something needs to be arranged, by the team and by their reporting manager, to best use their skills productively. Ideally something 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.