Lista de tags SQL e filtragem de tags

left join as tags table e inclua o id que está sendo pesquisado na cláusula de junção e verifique as contagens em having .

SELECT u.id,u.name,GROUP_CONCAT(ut.tagid) as tags
FROM users u 
LEFT JOIN usertag as ut ON u.id = ut.userid 
LEFT JOIN tags t ON t.id=ut.tagid AND t.ID IN (10,20,30) --change this as needed
GROUP BY u.id,u.name
HAVING COUNT(ut.tagid) >= COUNT(t.id) AND COUNT(t.id) = 3 --change this number to the number of tags

Mais uma opção é usar FIND_IN_SET se houver valores limitados. Por exemplo,

SELECT * FROM (
SELECT u.*, GROUP_CONCAT(ut.tagid) as tags 
FROM users as u 
LEFT JOIN usertag as ut ON u.id = ut.userid 
GROUP BY u.id
) T
WHERE FIND_IN_SET('10',tags) > 0 AND FIND_IN_SET('20',tags) > 0