Identity Server 3 - 401 on Ajax Calls instead of 302

In your example the UseCookieAuthentication no longer controls this, instead the UseOpenIdConnectAuthentication does. This involves using the Notifications property and intercepting OpenID Connect authentication requests.

Try out the following for inspiration:

app.UseOpenIdConnectAuthentication(new OpenIdConnectAuthenticationOptions
{
    Authority = IdentityConfig.Authority,
    ClientId = IdentityConfig.SoftwareClientId,
    Scope = "openid profile roles",
    RedirectUri = IdentityConfig.RedirectUri,
    ResponseType = "id_token",
    SignInAsAuthenticationType = "Cookies",
    Notifications = new OpenIdConnectAuthenticationNotifications
    {
        RedirectToIdentityProvider = notification =>
        {
            if (notification.ProtocolMessage.RequestType == OpenIdConnectRequestType.AuthenticationRequest)
            {
                if (IsAjaxRequest(notification.Request) && notification.Response.StatusCode == (int)HttpStatusCode.Unauthorized)
                {
                    notification.Response.StatusCode = (int)HttpStatusCode.Unauthorized;
                    notification.HandleResponse();
                    return Task.FromResult(0);
                }
            }
            return Task.FromResult(0);
        }
    }
});