Update June 28: Rabbi Jason Miller, the author of the June 23 Huffington Post article, "Delta Adopts Saudi Arabian Airlines' No-Jew Policy," wrote another article June 27, stating the headline of the original article was "sensational" and "misleading."
Miller writes in the latest article: "Delta did not adopt Saudi Arabia's policy and Delta does not discriminate. In my article, I clearly stated that Delta does not discriminate but that my concern was that Delta was supporting membership in the SkyTeam Alliance by an airline run by a discriminatory country."
Miller points out that Delta Air Lines' original response, once the controversy broke out, was to basically say that if Saudi Arabia improperly withholds travel documents for U.S. citizens, then people should take up that issue with the U.S. State Department.
Only on June 24, after the controversy went viral, Miller notes, did Delta Air Lines issued a stronger statement, explaining that it has no intention to codeshare with Saudi Arabian Airlines.
Meanwhile, the Religious News Service, which ran a story in the Huffington Post June 24 entitled, "Delta Partnership May Cause Travel Headaches For Non-Muslims," apologized for the story and said it contained incomplete information. RNS noted Delta doesn't intend to codeshare or share reciprocal benefits with Saudi Arabian Airlines."
Update: The government of Saudi Arabia has weighed in on the controversy surrounding Delta Air Lines and Saudi Arabian Airlines' entry into SkyTeam:
The Kingdom of Saudi Arabia states: "Rumors being circaulated via the Internet regarding passenger flight restrictions on Saudi Arabian Airlines are completely false. The Government of Saudi Arabia does not deny visas to U.S. citizens based on their religion."
The Saudi government does not address the issue of whether it denies visas to U.S. citizens with Israeli stamps in their passports or how their policies relate to citizens of other countries.
And, in other developments, the Anti-Defamation League called on Delta Air Lines, United Airlines "and other American carriers who service Saudi Arabian destinations either on their own or through codeshare partnerships" to ensure that their passengers don't face discrimination because of Saudi policies.
In a statement released this afternoon, Delta Air Lines indicated that it doesn't intend to codeshare with Saudi Arabian Airlines or share reciprocal benefits, but will interline with the airline.
Here's Delta's statement:

Delta Air Lines does not discriminate nor do we condone discrimination against any of our customers in regards to age, race, nationality, religion, or gender.
Delta does not operate service to Saudi Arabia and does not codeshare with any airline that serves that country. Delta does not intend to codeshare or share reciprocal benefits, such as frequent flier benefits, with Saudi Arabian Airlines, which we have confirmed with SkyTeam, an Amsterdam-based 14-member global airline alliance.
Delta’s only agreement with Saudi Arabian Airlines is a standard industry interline agreement, which allows passengers to book tickets on multiple carriers, similar to the standard interline agreements American Airlines, US Airways and Alaska Airlines have with Saudi Arabian Airlines.
All of the three global airline alliances -- Star, which includes United Airlines; oneworld, which includes American Airlines, and SkyTeam, which includes Delta -- have members that fly to Saudi Arabia and are subject to that country’s rules governing entry.
The original post follows:
Just weeks after Delta Air Lines came under fire for its now-revised bag policy for U.S. soldiers, the airline is defending itself again, this time over Saudi Arabian Airlines' 2012 entry into the SkyTeam alliance.
In a June 23 Huffington Post article, Delta Adopts Saudi Arabian Airlines' No Jew Policy, Rabbi Jason Miller writes that Saudi Arabian Airlines' entry into SkyTeam means Delta, which also is a SkyTeam member, would have "to ban Jews and holders of Israeli passports from boarding flights to Saudi Arabia."
It should be pointed out that anyone with an Israeli stamp in their passport would face issues, as well.
On social media airwaves, Delta has been the brunt of intense criticism about the new partnership since yesterday, when the Huffington Post article appeared.
For example, Larry_slo tweeted June 24: "@DeltaAssist Your blog doesn't say you are not banning Jews, it just says it is someone else's fault. That is sick."
The Delta Twitter team has been referring outraged Twitterati to a June 23 Delta Air Line Blog post, entitled View from 30,000 feet: Delta on Diversity.
Writing in the blog, Trebor Banstetter, a Delta spokesman, acknowledged the barrage of criticism, adding:

For this particular concern, it is important to realize that visa requirements to enter any country are dictated by that nation's government, not the airlines, and they apply to anyone entering the country regardless of whether it's by plane, bus or train.
Thus, Delta doesn't reject the allegations in the Huffington Post article as being inaccurate, but essentially says that Saudi Arabia's antisemitic policies are out of the airline's hands.
Banstetter writes that Delta doesn't discriminate on the basis of "age, race, nationality, religion, or gender," and that he's proud to work for an airline as diverse as Delta.
As a member of SkyTeam, of course, Delta benefits from the entry of the new SkyTeam partner. Saudi Arabian Airlines adds 35 destinations to the alliance.
Unlike in the case of the U.S. soldiers returning from Afghanistan and getting charged for fourth checked bags, there is no indication of a policy change from Delta.
Delta hasn't publicly called for a reversal of SkyTeam's decision to welcome Saudi Arabian Airlines next year.
It is interesting to note that the same fury directed against Delta might also be leveled against the other SkyTeam members, including Aeroflot, Aeromexico, AirEuropa, Air France, Alitalia, China Eastern, China Southern, Czech Airlines, Kenya Airways, KLM, Korean Air, Tarom and Vietnam Airlines.
Saudi Arabian Airlines would be the first SkyTeam member from the Middle East.
It should be pointed out that OneWorld, which counts American Airlines among its members, and the Star Alliance (including United, Continental, US Airways and Luthansa etc.) also fly to Saudi Arabia.
Delta may be on the hotseat now because Saudi Arabian Airlines' entry into SkyTeam was announced several months ago and its implementation is upcoming.
Asked whether Delta would bar Jews and Israelis on codeshare flights headed to Saudi Arabia, spokeswoman Susan Elliott says:

It doesn’t matter where the flight is going. If someone has a ticket, proper documentation and has passed the mandated security screening, we welcome them onboard.
Elliott adds: "The idea that we are banning Jews from our flights is offensive to a lot of us at Delta."