I need to retrieve certain rows from a table depending on certain values in a specific column, named columnX in the example:
select *
from t
If you are only going to search lists of one-character values, then split each string into an array of characters and index the array:
CREATE INDEX
ix_tablename_columnxlist
ON tableName
USING GIN((REGEXP_SPLIT_TO_ARRAY(columnX, '')))
then search against the index:
SELECT *
FROM tableName
WHERE REGEXP_SPLIT_TO_ARRAY(columnX, '') && ARRAY['A', 'B', 'C', '1', '2', '3']