MySQL 8.0

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

CREATE TABLE test (id INT, val JSON) 
SELECT 1 id, '{"a": true, "b":true, "c":false, "d":true}' val UNION ALL
SELECT 2, '{"a": true, "b":false, "c":true, "d":false}' UNION ALL
SELECT 3, '{"a": false, "b":true, "c":false, "d":true}' UNION ALL
SELECT 4, '{"a": false, "b":false, "c":false, "d":false}';   
SELECT id,
       val, 
       REGEXP_REPLACE(REGEXP_REPLACE(val, '(, *)?"[^"]+": *false', ''), '\\{ *, *', '\\{') without_false
FROM test


id
val
without_false


1
{"a": true, "b": true, "c": false, "d": true}
{"a": true, "b": true, "d": true}

2
{"a": true, "b": false, "c": true, "d": false}
{"a": true, "c": true}

3
{"a": false, "b": true, "c": false, "d": true}
{"b": true, "d": true}

4
{"a": false, "b": false, "c": false, "d": false}
{}


WITH RECURSIVE
cte AS ( SELECT id, val src, val FROM test
         UNION ALL
         SELECT id, 
                src,
                JSON_REMOVE(val, JSON_UNQUOTE(JSON_SEARCH(REPLACE(val, 'false', '"false"'), 'one', 'false')))
         FROM cte
         WHERE JSON_SEARCH(REPLACE(val, 'false', '"false"'), 'one', 'false') IS NOT NULL
         )
SELECT id, src val, val without_false
FROM cte
WHERE JSON_SEARCH(REPLACE(val, 'false', '"false"'), 'one', 'false') IS NULL


id
val
without_false


1
{"a": true, "b": true, "c": false, "d": true}
{"a": true, "b": true, "d": true}

2
{"a": true, "b": false, "c": true, "d": false}
{"a": true, "c": true}

3
{"a": false, "b": true, "c": false, "d": true}
{"b": true, "d": true}

4
{"a": false, "b": false, "c": false, "d": false}
{}

id	val	without_false
1	{"a": true, "b": true, "c": false, "d": true}	{"a": true, "b": true, "d": true}
2	{"a": true, "b": false, "c": true, "d": false}	{"a": true, "c": true}
3	{"a": false, "b": true, "c": false, "d": true}	{"b": true, "d": true}
4	{"a": false, "b": false, "c": false, "d": false}	{}