There are some differences in behavior between .NET Framework (Desktop) and .NET Core which are causing these tests to fail:

xUnit.net Console Runner (64-bit .NET 4.0.30319.42000)
Discovering: System.Net.Requests.Tests
Discovered: System.Net.Requests.Tests
Starting: System.Net.Requests.Tests
System.Net.Tests.HttpWebRequestHeaderTest.Ctor_VerifyHttpRequestDefaults(remoteServer: http://corefx-net.cloudapp.net/Echo.ashx) [FAIL]
Assert.Equal() Failure
Expected: 0
Actual: 64
Stack Trace:
s:\GitHub\corefx\src\System.Net.Requests\tests\HttpWebRequestHeaderTest.cs(32,0): at System.Net.Tests.HttpWebRequestHeaderTest.Ctor_VerifyHttpRequest
Defaults(Uri remoteServer)
System.Net.Tests.HttpWebRequestHeaderTest.HttpWebRequest_ServicePoint_Throws(remoteServer: http://corefx-net.cloudapp.net/Echo.ashx) [FAIL]
Assert.Throws() Failure
Expected: typeof(System.PlatformNotSupportedException)
Actual: (No exception was thrown)
Stack Trace:
s:\GitHub\corefx\src\System.Net.Requests\tests\HttpWebRequestHeaderTest.cs(81,0): at System.Net.Tests.HttpWebRequestHeaderTest.HttpWebRequest_Service
Point_Throws(Uri remoteServer)
System.Net.Tests.HttpWebRequestHeaderTest.HttpWebRequest_ServicePoint_Throws(remoteServer: https://corefx-net.cloudapp.net/Echo.ashx) [FAIL]
Assert.Throws() Failure
Expected: typeof(System.PlatformNotSupportedException)
Actual: (No exception was thrown)
Stack Trace:
s:\GitHub\corefx\src\System.Net.Requests\tests\HttpWebRequestHeaderTest.cs(81,0): at System.Net.Tests.HttpWebRequestHeaderTest.HttpWebRequest_Service
Point_Throws(Uri remoteServer)
System.Net.Tests.HttpWebResponseHeaderTest.HttpWebResponse_Close_Success [FAIL]
Assert.Throws() Failure
Expected: typeof(System.ObjectDisposedException)
Actual: (No exception was thrown)