It looks like the IdentityTypes property is not a $list, but a list collection. You can read more about those here: https://docs.intersystems.com/irislatest/csp/docbook/DocBook.UI.Page.cls... 

To use list collections in .NET IRIS Native, you treat them like any other IRISObject.

Your sample code would now look something like this

IRIS iris = IRIS.CreateIRIS(conn);
IRISObject OidMap = (IRISObject)iris.ClassMethodObject("HS.Data.OIDMap","%New");
var oType = iris.ClassMethodObject("HS.Data.OIDType","%OpenId","Device");

// new code
IRISObject newList = (IRISObject)iris.ClassMethodObject("%ListOfDataTypes", "%New");
newList.InvokeVoid("Insert", oType);
OidMap.Set("IdentityTypes",newList);

Also, you don't need to instantiate the list directly, and can get it by accessing the existing property instead

IRISObject list = (IRISObject)OidMap.GetObject("IdentityTypes")
list.InvokeVoid("Insert",oType);

We're currently working on getting our .NET packages posted on NuGet, @Stefan Wittmann has the latest details.

We also currently ship both .dll and .nupkg files for each of our .NET projects with IRIS, so you can use those nupkg files in the meantime. 

If you're not getting the IRIS Security Error every time, only when there's multiple calls, then it's possible you're exceeding your license's allowed number of concurrent connections, so I would check there first. 

Also, the call to IRISPoolManager.RemoveAllIdleConnections() will remove any connections that have been closed but are still in the pool. Calling this after every Connection.Close() will undo any advantages of connection pooling. If you want to disable pooling, you can add "Pooling = False" to the connection string, then the call is unnecessary. If you want to use pooling, you should remove the call to RemoveAllIdleConnections().