SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    23051, 23066, 23061, 23038, 23037, 23050, 
    23045, 23032, 23073, 23052, 23023, 
    23056, 23057, 23065, 23064, 23069, 
    23044
  ) 
  AND category_id != 1

Query time 0.00006

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_categories",
          "access_type": "range",
          "possible_keys": ["PRIMARY", "parent", "p_category_id"],
          "key": "parent",
          "key_length": "3",
          "used_key_parts": ["parent_id"],
          "rows": 42,
          "filtered": 100,
          "index_condition": "cscart_categories.parent_id in (23051,23066,23061,23038,23037,23050,23045,23032,23073,23052,23023,23056,23057,23065,23064,23069,23044)",
          "attached_condition": "cscart_categories.category_id <> 1"
        }
      }
    ]
  }
}