MySQL 8.0

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create table your_table (data text)
insert into your_table values
  ('{"homeWidgetToShow":"chat_and_notes","official":false,"nationalFederation":false,"categories":[],"activities":{"0":2,"2":7,"1":3},"clubsBlackList":[],"privateMembers":false,"alwaysShowDescription":false,"restrictMembersFromPositingForums":false}'),
  ('{"homeWidgetToShow":"chat_and_notes","official":false,"nationalFederation":false,"categories":[],"clubsBlackList":[],"privateMembers":false,"alwaysShowDescription":false,"restrictMembersFromPositingForums":false}'),
  ('{"homeWidgetToShow":"chat_and_notes","official":false,"nationalFederation":false,"categories":[],"activities":{"0":2,"2":3,"1":2},"clubsBlackList":[],"privateMembers":false,"alwaysShowDescription":false,"restrictMembersFromPositingForums":false}'),
  ('{"homeWidgetToShow":"chat_and_notes","official":false,"nationalFederation":false,"categories":[],"activities":{"0":2,"2":7,"1":5},"clubsBlackList":[],"privateMembers":false,"alwaysShowDescription":false,"restrictMembersFromPositingForums":false}')

Records: 4  Duplicates: 0  Warnings: 0


SELECT *
FROM your_table
WHERE 3 MEMBER OF(data->>'$.activities.*')


data


{"homeWidgetToShow":"chat_and_notes","official":false,"nationalFederation":false,"categories":[],"activities":{"0":2,"2":7,"1":3},"clubsBlackList":[],"privateMembers":false,"alwaysShowDescription":false,"restrictMembersFromPositingForums":false}

{"homeWidgetToShow":"chat_and_notes","official":false,"nationalFederation":false,"categories":[],"activities":{"0":2,"2":3,"1":2},"clubsBlackList":[],"privateMembers":false,"alwaysShowDescription":false,"restrictMembersFromPositingForums":false}