Reproduced this with SQL server.
Added your Material class. Correction to you keys were made.
The HasValue as stated was fine. Also Convert.ToBoolean helped with translation.
Some options for various results have been provided.
       [HttpGet] Â
       public IActionResult GetNulls()
       {
           List<Material> mats = new List<Material>
           {
               new Material { MaterialID = 1, StockQty = 10, FlagForDelete = true },
               new Material { MaterialID = 2, StockQty = 20, FlagForDelete = false },
               new Material { MaterialID = 3, StockQty = 30 }
           };
           string Response = "SUCCESS:";
           try
           {
               List<Material> NotFalse = mats.Where(m => m.FlagForDelete != Convert.ToBoolean(false)).ToList();
               List<Material> NotTrue = mats.Where(m => m.FlagForDelete != Convert.ToBoolean(true)).ToList();
               List<Material> NotEither = mats.Where(m => m.FlagForDelete != Convert.ToBoolean(true) &&  m.FlagForDelete != Convert.ToBoolean(false)).ToList();
               List<Material> Lakemann = mats.Where(m => !m.FlagForDelete.HasValue).ToList();
               var combine = new { NotFalse, NotTrue, NotEither , Lakemann };
               var options = new JsonSerializerOptions { WriteIndented = true };
               string json = JsonSerializer.Serialize(combine, options);
               return Ok(json);
           }
           catch (Exception ex)
           {Response = "ERROR: **" + ex.Message;}
           finally
           {};
           return NoContent();
       }
JSON
{
 "NotFalse": [
   {
     "MaterialID": 1,
     "StockQty": 10,
     "FlagForDelete": true
   },
   {
     "MaterialID": 3,
     "StockQty": 30,
     "FlagForDelete": null
   }
 ],
 "NotTrue": [
   {
     "MaterialID": 2,
     "StockQty": 20,
     "FlagForDelete": false
   },
   {
     "MaterialID": 3,
     "StockQty": 30,
     "FlagForDelete": null
   }
 ],
 "NotEither": [
   {
     "MaterialID": 3,
     "StockQty": 30,
     "FlagForDelete": null
   }
 ],
 "Lakemann": [
   {
     "MaterialID": 3,
     "StockQty": 30,
     "FlagForDelete": null
   }
 ]
}