SELECT 
  category_id, 
  parent_id 
FROM 
  jmj_categories 
WHERE 
  parent_id IN(
    100, 89, 92, 97, 93, 98, 90, 101, 91, 94, 
    99, 102, 103, 95, 96
  ) 
  AND category_id != 1

Query time 0.00059

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "29.42"
    },
    "table": {
      "table_name": "jmj_categories",
      "access_type": "ALL",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "rows_examined_per_scan": 120,
      "rows_produced_per_join": 24,
      "filtered": "20.00",
      "cost_info": {
        "read_cost": "24.62",
        "eval_cost": "4.80",
        "prefix_cost": "29.42",
        "data_read_per_join": "93K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "((`jmj_test`.`jmj_categories`.`parent_id` in (100,89,92,97,93,98,90,101,91,94,99,102,103,95,96)) and (`jmj_test`.`jmj_categories`.`category_id` <> 1))"
    }
  }
}