How can I get a random number generated in a CTE not to change in JOIN?

The problem

I'm generating a random number for each row in a table #Table_1 in a CTE, using this technique. I'm then joining the results of the CTE on another table, #Table_2. Instead of getting a random number for each row in #Table_1, I'm getting a new random number for every resulting row in the join!

CREATE TABLE #Table_1 (Id INT)

CREATE TABLE #Table_2 (MyId INT, ParentId INT)

INSERT INTO #Table_1
VALUES (1), (2), (3)

INSERT INTO #Table_2
VALUES (1, 1), (2, 1), (3, 1), (4, 1), (1, 2), (2, 2), (3, 2), (1, 3)


;WITH RandomCTE AS
(
    SELECT Id, (ABS(CHECKSUM(NewId())) % 5)RandomNumber
    FROM #Table_1
)
SELECT *
FROM RandomCTE r
INNER JOIN #Table_2 t
    ON r.Id = t.ParentId

The results

Id          MyId        RandomNumber
----------- ----------- ------------
1           1           1
1           2           2
1           3           0
1           4           3
2           1           4
2           2           0
2           3           0
3           1           3

The desired results

Id          MyId        RandomNumber
----------- ----------- ------------
1           1           1
1           2           1
1           3           1
1           4           1
2           1           4
2           2           4
2           3           4
3           1           3

What I tried

I tried to obscure the logic of the random number generation from the optimizer by casting the random number to VARCHAR, but that did not work.

What I don't want to do

I'd like to avoid using a temporary table to store the results of the CTE.

How can I generate a random number for a table and preserve that random number in a join without using temporary storage?