如果你想重用HttpClient，建议不要使用DefaultRequestHeaders，因为它们是用来发送每个请求的。

你可以试试这个:

var requestMessage = new HttpRequestMessage
    {
        Method = HttpMethod.Post,
        Content = new StringContent("...", Encoding.UTF8, "application/json"),
        RequestUri = new Uri("...")
    };

requestMessage.Headers.Authorization = new AuthenticationHeaderValue("Basic", 
    Convert.ToBase64String(System.Text.ASCIIEncoding.ASCII.GetBytes($"{user}:{password}")));

var response = await _httpClient.SendAsync(requestMessage);

使用System.Net.Http程序集的AuthenticationHeaderValue类

public AuthenticationHeaderValue(
    string scheme,
    string parameter
)

我们可以像这样设置或更新httpclient现有的授权头:

httpclient.DefaultRequestHeaders.Authorization = new AuthenticationHeaderValue("Bearer", TokenResponse.AccessToken);

你也可以使用下面的例子，它使用IHttpClientFactory:

    readonly IHttpClientFactory _httpClientFactory;
    
    public HTTPClientHelper(IHttpClientFactory httpClientFactory, string clientName = null)
    {
        this._httpClientFactory = httpClientFactory;
    }

    public Task<T> GetAsync(string url, string token) {

        var client = _httpClientFactory.CreateClient(_clientName);

        client.DefaultRequestHeaders.Authorization = new AuthenticationHeaderValue(JwtBearerDefaults.AuthenticationScheme, token);

        using (HttpResponseMessage response = await _client.GetAsync(url)){
          ......
        }
     }

使用现有的库可能更容易。

例如，Identity Server 4中添加了下面的扩展方法 https://www.nuget.org/packages/IdentityModel/

 public static void SetBasicAuthentication(this HttpClient client, string userName, string password);
    //
    // Summary:
    //     Sets a basic authentication header.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   userName:
    //     Name of the user.
    //
    //   password:
    //     The password.
    public static void SetBasicAuthentication(this HttpRequestMessage request, string userName, string password);
    //
    // Summary:
    //     Sets a basic authentication header for RFC6749 client authentication.
    //
    // Parameters:
    //   client:
    //     The client.
    //
    //   userName:
    //     Name of the user.
    //
    //   password:
    //     The password.
    public static void SetBasicAuthenticationOAuth(this HttpClient client, string userName, string password);
    //
    // Summary:
    //     Sets a basic authentication header for RFC6749 client authentication.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   userName:
    //     Name of the user.
    //
    //   password:
    //     The password.
    public static void SetBasicAuthenticationOAuth(this HttpRequestMessage request, string userName, string password);
    //
    // Summary:
    //     Sets an authorization header with a bearer token.
    //
    // Parameters:
    //   client:
    //     The client.
    //
    //   token:
    //     The token.
    public static void SetBearerToken(this HttpClient client, string token);
    //
    // Summary:
    //     Sets an authorization header with a bearer token.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   token:
    //     The token.
    public static void SetBearerToken(this HttpRequestMessage request, string token);
    //
    // Summary:
    //     Sets an authorization header with a given scheme and value.
    //
    // Parameters:
    //   client:
    //     The client.
    //
    //   scheme:
    //     The scheme.
    //
    //   token:
    //     The token.
    public static void SetToken(this HttpClient client, string scheme, string token);
    //
    // Summary:
    //     Sets an authorization header with a given scheme and value.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   scheme:
    //     The scheme.
    //
    //   token:
    //     The token.
    public static void SetToken(this HttpRequestMessage request, string scheme, string token);

这可以工作，如果你从服务接收到一个json或xml，我认为这可以给你一个关于标题和T类型如何工作的想法，如果你使用函数MakeXmlRequest(把结果放在xmldocumentnet)和MakeJsonRequest(把json放在类你希望有相同的结构，json响应)在下一种方式

/*-------------------------example of use-------------*/
MakeXmlRequest<XmlDocument>("your_uri",result=>your_xmlDocument_variable =     result,error=>your_exception_Var = error);

MakeJsonRequest<classwhateveryouwant>("your_uri",result=>your_classwhateveryouwant_variable=result,error=>your_exception_Var=error)
/*-------------------------------------------------------------------------------*/


public class RestService
{
    public void MakeXmlRequest<T>(string uri, Action<XmlDocument> successAction, Action<Exception> errorAction)
    {
        XmlDocument XMLResponse = new XmlDocument();
        string wufooAPIKey = ""; /*or username as well*/
        string password = "";
        StringBuilder url = new StringBuilder();
        url.Append(uri);
        HttpWebRequest request = (HttpWebRequest)HttpWebRequest.Create(url.ToString());
        string authInfo = wufooAPIKey + ":" + password;
        authInfo = Convert.ToBase64String(Encoding.Default.GetBytes(authInfo));
        request.Timeout = 30000;
        request.KeepAlive = false;
        request.Headers["Authorization"] = "Basic " + authInfo;
        string documento = "";
        MakeRequest(request,response=> documento = response,
                            (error) =>
                            {
                             if (errorAction != null)
                             {
                                errorAction(error);
                             }
                            }
                   );
        XMLResponse.LoadXml(documento);
        successAction(XMLResponse);
    }



    public void MakeJsonRequest<T>(string uri, Action<T> successAction, Action<Exception> errorAction)
    {
        string wufooAPIKey = "";
        string password = "";
        StringBuilder url = new StringBuilder();
        url.Append(uri);
        HttpWebRequest request = (HttpWebRequest)HttpWebRequest.Create(url.ToString());
        string authInfo = wufooAPIKey + ":" + password;
        authInfo = Convert.ToBase64String(Encoding.Default.GetBytes(authInfo));
        request.Timeout = 30000;
        request.KeepAlive = false;
        request.Headers["Authorization"] = "Basic " + authInfo;
       // request.Accept = "application/json";
      //  request.Method = "GET";
        MakeRequest(
           request,
           (response) =>
           {
               if (successAction != null)
               {
                   T toReturn;
                   try
                   {
                       toReturn = Deserialize<T>(response);
                   }
                   catch (Exception ex)
                   {
                       errorAction(ex);
                       return;
                   }
                   successAction(toReturn);
               }
           },
           (error) =>
           {
               if (errorAction != null)
               {
                   errorAction(error);
               }
           }
        );
    }
    private void MakeRequest(HttpWebRequest request, Action<string> successAction, Action<Exception> errorAction)
    {
        try{
            using (var webResponse = (HttpWebResponse)request.GetResponse())
            {
                using (var reader = new StreamReader(webResponse.GetResponseStream()))
                {
                    var objText = reader.ReadToEnd();
                    successAction(objText);
                }
            }
        }catch(HttpException ex){
            errorAction(ex);
        }
    }
    private T Deserialize<T>(string responseBody)
    {
        try
        {
            var toReturns = JsonConvert.DeserializeObject<T>(responseBody);
             return toReturns;
        }
        catch (Exception ex)
        {
            string errores;
            errores = ex.Message;
        }
        var toReturn = JsonConvert.DeserializeObject<T>(responseBody);
        return toReturn;
    }
}
}

6年过去了，但为了帮助别人，我加了这个。

https://www.codeproject.com/Tips/996401/Authenticate-WebAPIs-with-Basic-and-Windows-Authen

var authenticationBytes = Encoding.ASCII.GetBytes("<username>:<password>");
using (HttpClient confClient = new HttpClient())
{
  confClient.DefaultRequestHeaders.Authorization = new AuthenticationHeaderValue("Basic", 
         Convert.ToBase64String(authenticationBytes));
  confClient.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue(Constants.MediaType));  
  HttpResponseMessage message = confClient.GetAsync("<service URI>").Result;
  if (message.IsSuccessStatusCode)
  {
    var inter = message.Content.ReadAsStringAsync();
    List<string> result = JsonConvert.DeserializeObject<List<string>>(inter.Result);
  }
}