Sites that use cross site resource will still work. Except the cross domain resource provider will always see the same domain coming to get resource.

For example, if you are on Site A and use cross site resource from Site C. The site C will get a cookie C('A)

And in another day, you visited a Site B that also use resource from Site C. The site C get a cookie C('B).

And C('A) != C('B)

Although these cookie are both issued by Site C. They are associated to different first party domain and can't be connected directly.

It's just like you open a private browser session for every site you visit.

I think it is a extension usage from Firefox's container technology.