If I've understood the code correctly, there are some worrying changes in System.Xml. There are minor niggles, such as the disappearance of Close(), but that's not a major headache. Some members relating to System.Xml.Schema have gone, which means it will be difficult to support schema-aware processing (more below).
The loss of XmlResolver as a public class is most definitely in the category of "blocking issue". XmlResolver is now internal and appears to have a single concrete implementation which can only resolve URLs to files on the file system. It's the mechanism we use for resolving DTDs, XSDs, XQuery modules, XSLT files and probably much more besides.
On the one hand, it's always been a bit of a frustrating class. The "role" attribute never got used. It would have been nice to be informed whether a resolver was resolving a PUBLIC or SYSTEM identifier, or whether it was resolving a DTD or an XSLT file included from another transform.
As an aside, there have been other annoying breaking changes in .NET 4.5.2 in this area, such as the case of the mysteriously disappearing external entities.
I had thought that this was largely intact until I discovered that XPathItem's default constructor is now internal. That means we can't derive XPathAtomicValue, XPathFunctionItem, XPathMap and XPathArray, the classes representing the XPath and XQuery data model items.
If we can't use XPathItem as a base class, that pretty much rules out using XPathNavigator, which in turn pretty much rules out using System.Xml.XPath at all as things stand.
This is gone. In a sense that's a good thing, as it gives us a clean slate to produce a fully compliant XSD 1.0 and XSD 1.1 implementation, but that's no small task. In the meantime, we could implement just enough to support non-schema aware processing.
This is gone, and was the main reason for us wanting to port XmlPrime.
In summary, there seems to have been quite a bit of damage done to .NET's XML handling, and unless I'm mistaken or some of the issues given above are addressed, it will be a while before we can port to .NET Core.