I would look at the Join operator:
from r in list join i in listofIds on r.Id equals i select r
I'm not sure how this would be optimized over the Contains methods, but at least it gives the compiler a better idea of what you're trying to do. It's also sematically closer to what you're trying to achieve.
Edit: Extension method syntax for completeness (now that I've figured it out):
var results = listofIds.Join(list, i => i, r => r.Id, (i, r) => r);