This was mentioned in the very long thread about the new delta.com, but it is apt to get lost in there.
The website now says that if you are flying FC you get SkyClub entry. Of course, this was always true if you have an international flight that day but there is no such restriction mentioned.
Instead, it reads:
The First Class Treatment
A First Class travel experience begins long before you board your aircraft. That's why all First Class passengers automatically receive our two most premium airport services.
Delta Sky Priority®
Being Sky Priority means getting a heightened level of service that gets you where you’re going — faster and easier. Speedy check-in, accelerated security, priority boarding and an exclusive reservation line are just a few of the perks we provide. Explore Delta Sky Priority
Delta Sky Club®
Spend your time between flights in an award-winning Delta Sky Club. With complimentary beer, wine, spirits and snacks served all day, free Wi-Fi and a hot shower in select locations, you have a place to call home, no matter what city you find yourself in. Explore Delta Sky Club
Is this now the case or is it just a mistake on the website?
As a non-US resident, this would be good for me. I get SkyClub entry on days when I am flying internationally (both because of my Elite+ status and the fact that I take Biz/FC itineraries).
It would be ridiculous for me to buy a SkyClub membership for those very few days each year when I am on domestic U.S. flights without having an international segment.
My next itinerary, for example, is TLV-JFK, JFK-LAS, LAS-ATL, and ATL-JFK-TLV.
I will get SkyClub entry for all segments except JFK-LAS and LAS-ATL as I won't be flying to/from Israel on those days. Of course, LAS has no SkyClub, so in real life the only time I will miss out is before my JFK-LAS flight.
If this is not a mistake, and is really the case, I will be able to use the SkyClub in JFK that day.
I only see this text under the BusinessElite section on the website. Perhaps OP could provide a link? At any rate, I see no evidence that DL has changed their policy in the Sky Club entrance rules.
Edit to add - I think the text used to be on this page (I get a hit when doing a search) --
they actually were on the phone last night from the LAX sky club with delta it support on the issue. Apparently the club matrons noticed it or had a f class flyer attempt to use it on day one. Might have something to do with its disappearance between last night and this am.