Intersecting List with keys of Map

You can stream set of entries:

map.entrySet().stream()
    .filter(e -> list.contains(e.getKey()))
    .collect(toMap(Map.Entry::getKey, Map.Entry::getValue));

If you also want to map keys to id field, then:

map.entrySet().stream()
    .filter(e -> list.contains(e.getKey()))
    .collect(toMap(e -> e.getKey().getId(), Map.Entry::getValue));