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 
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') 
WHERE 
  q_products_categories.product_id IN (
    6137, 6138, 6139, 6140, 6141, 6142, 6143, 
    6144, 6145, 6146, 6147, 6148, 6149, 
    6150, 6151, 6152
  ) 
GROUP BY 
  q_products_categories.product_id

Query time 0.00078

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "62.81"
    },
    "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": 18,
            "rows_produced_per_join": 18,
            "filtered": "100.00",
            "index_condition": "(`portal`.`q_products_categories`.`product_id` in (6137,6138,6139,6140,6141,6142,6143,6144,6145,6146,6147,6148,6149,6150,6151,6152))",
            "cost_info": {
              "read_cost": "37.61",
              "eval_cost": "3.60",
              "prefix_cost": "41.21",
              "data_read_per_join": "288"
            },
            "used_columns": [
              "product_id",
              "category_id",
              "link_type"
            ]
          }
        },
        {
          "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": 3,
            "filtered": "20.00",
            "cost_info": {
              "read_cost": "18.00",
              "eval_cost": "0.72",
              "prefix_cost": "62.81",
              "data_read_per_join": "9K"
            },
            "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
6137 402M
6138 402M
6139 193,199,402M
6140 193,402M
6141 193,199,402M
6142 193,402M
6143 193,402M
6144 193,402M
6145 193,402M
6146 193,402M
6147 193,402M
6148 193,402M
6149 193,402M
6150 193,402M
6151 193,402M
6152 402M