SELECT 
  q_products_categories.product_id, 
  GROUP_CONCAT(
    IF(
      q_products_categories.link_type = "M", 
      CONCAT(
        q_products_categories.category_id, 
        "M"
      ), 
      q_products_categories.category_id
    )
  ) AS category_ids, 
  product_position_source.position AS position 
FROM 
  q_products_categories 
  INNER JOIN q_categories ON q_categories.category_id = q_products_categories.category_id 
  AND (
    q_categories.usergroup_ids = '' 
    OR FIND_IN_SET(0, q_categories.usergroup_ids) 
    OR FIND_IN_SET(1, q_categories.usergroup_ids)
  ) 
  AND q_categories.status IN ('A', 'H') 
  LEFT JOIN q_products_categories AS product_position_source ON q_products_categories.product_id = product_position_source.product_id 
  AND product_position_source.category_id = 3 
WHERE 
  q_products_categories.product_id IN (
    611, 612, 613, 614, 615, 616, 581, 582, 
    583, 584, 585, 586, 565, 566, 567, 568, 
    569, 570, 571, 572, 573, 574, 575, 576, 
    577, 578, 579, 580, 551, 552
  ) 
GROUP BY 
  q_products_categories.product_id

Query time 0.00094

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "144.01"
    },
    "grouping_operation": {
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "q_products_categories",
            "access_type": "range",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "pt",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "rows_examined_per_scan": 30,
            "rows_produced_per_join": 30,
            "filtered": "100.00",
            "index_condition": "(`portal`.`q_products_categories`.`product_id` in (611,612,613,614,615,616,581,582,583,584,585,586,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,551,552))",
            "cost_info": {
              "read_cost": "66.01",
              "eval_cost": "6.00",
              "prefix_cost": "72.01",
              "data_read_per_join": "480"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        },
        {
          "table": {
            "table_name": "product_position_source",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "pt"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id",
              "product_id"
            ],
            "key_length": "6",
            "ref": [
              "const",
              "portal.q_products_categories.product_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 30,
            "filtered": "100.00",
            "cost_info": {
              "read_cost": "30.00",
              "eval_cost": "6.00",
              "prefix_cost": "108.01",
              "data_read_per_join": "480"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "position"
            ]
          }
        },
        {
          "table": {
            "table_name": "q_categories",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "c_status",
              "p_category_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "category_id"
            ],
            "key_length": "3",
            "ref": [
              "portal.q_products_categories.category_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 6,
            "filtered": "20.00",
            "cost_info": {
              "read_cost": "30.00",
              "eval_cost": "1.20",
              "prefix_cost": "144.01",
              "data_read_per_join": "15K"
            },
            "used_columns": [
              "category_id",
              "usergroup_ids",
              "status"
            ],
            "attached_condition": "(((`portal`.`q_categories`.`usergroup_ids` = '') or find_in_set(0,`portal`.`q_categories`.`usergroup_ids`) or find_in_set(1,`portal`.`q_categories`.`usergroup_ids`)) and (`portal`.`q_categories`.`status` in ('A','H')))"
          }
        }
      ]
    }
  }
}

Result

product_id category_ids position
551 39M
552 39M
565 39M
566 5M
567 4M
568 4M
569 4M
570 4M
571 4M
572 4M
573 4M
574 4M
575 39M
576 39M
577 4M
578 4M
579 4M
580 4M
581 5M
582 5M
583 5M
584 5M
585 4M
586 5M
611 4M
612 5M
613 5M
614 4M
615 4M
616 4M