If 'core' stuff is optional, it's not core at all, it's optional. Core material is the core of something. So naming things 'core' is stupid if it's not the core of something.

Here, the .NET core libraries/frameworks are a different direction. They're not core, but they're not to be seen as 'optional'. They're to be seen as 'alternative' to .NET full. Not a great alternative today, as many features are lacking and they're really rushing things towards a pretty stupidly set deadline (when you're adding features to a RC2, you're not doing it right), but perhaps someday.

Asp.net is going to be as "supported" as webforms or winforms are, i.e. they will patch them but let them die. I don't think it's just an optional alternative.