As others have commented, it would be preferable to normalise the data and store individual dates in multiple rows of a linked table rather than in a single field. But assuming there's a valid reason this can't be done, the following will do what you've asked:
SELECT date_csv,
CASE WHEN CHAR_LENGTH(REPLACE(date_csv, ',', '')) = CHAR_LENGTH(date_csv) - 1
THEN /* date_csv has a single comma */
CURRENT_DATE >= SUBSTRING(date_csv, 1, INSTR(date_csv, ',') - 1)
AND CURRENT_DATE <= SUBSTRING(date_csv, INSTR(date_csv, ',') + 1)
ELSE /* date_csv has either no comma or multiple commas */
FIND_IN_SET(DATE_FORMAT(CURRENT_DATE,'%Y-%m-%d'), date_csv) > 0
END AS 'Test result'
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