var results = list2.Where(item => list1.Exists(id => id == item.Id)).ToList();

    public static class ExtensionMethods
    {
        public static List<MyObj> Get(this List<MyObj> items, List<string> ids)
        {
            // здесь может быть "громоздкий", зато более эффективный код
            return items.Where(item => ids.Exists(id => id == item.Id)).ToList();
        }
    }
...
var results = list2.Get(list1);

        public static List<MyObj> GetByIds(this List<MyObj> items, List<string> ids)
        {
             List<MyObj> res = new List<MyObj>();
             foreach (var item in items) {
                foreach (var id in ids) {
                    if (item.Id == id) {
                        res.Add(item);
                        break;
                    }
                }
            }
             return res;
        }

        public static IEnumerable<TResult> JoinSorted<TOuter, TInner, TKey, TResult>(
            this IEnumerable<TOuter> outer,
            IEnumerable<TInner> inner,
            Func<TOuter, TKey> outerKeySelector,
            Func<TInner, TKey> innerKeySelector,
            Func<TOuter, TInner, TResult> resultSelector
            )
        {
            var comparer = Comparer<TKey>.Default;
            using (var outerEnumerator = outer.GetEnumerator())
            using (var innerEnumerator = inner.GetEnumerator()) {
                bool outerCurr = outerEnumerator.MoveNext();
                bool innerCurr = innerEnumerator.MoveNext();
                while (outerCurr && innerCurr) {
                    int cr = comparer.Compare(outerKeySelector(outerEnumerator.Current), innerKeySelector(innerEnumerator.Current));
                    if (cr == 0) {
                        yield return resultSelector(outerEnumerator.Current, innerEnumerator.Current);
                        innerCurr = innerEnumerator.MoveNext();
                    } else if (cr < 0)
                        outerCurr = outerEnumerator.MoveNext();
                    else
                        innerCurr = innerEnumerator.MoveNext();
                }
            }
        }