Today, Edward Winter's invaluable Chess Notes web site has a photo from AVRO 1938 (scroll down to note # 7191) where Alekhine is seen chatting with Flohr during the tournament. Flohr, of course, was Jewish, and we see here that as late as 1938, at least, Alekhine not only had no problem playing with Jews, but obviously was friendly with them.
Another unexpected story of how Alekhine's antisemitic articles in fact helped at least one person survive during the holocaust has been given in Forward magazine in the article "Encounter with Alekhine" by Michael Feuer. The author's father, Otto Feuer, had found an article by Alekhine discarded in the camp's latrine:
One day, in the Buchenwald latrine, Otto came upon what he thought was a miracle of sorts: There on the ground was a page from a recent German chess magazine, undoubtedly discarded by an SS guard, with an article by, of all people, Alekhine. Otto’s mood soared — until he began reading. Then he discovered that Alekhine had become a rabid anti-Semite and Nazi sympathizer. The article was all about the evils of “Jewish chess.” Otto sank into an especially low depression. But then there was another uplift, because it occurred to him that if he was still capable of experiencing both joy and sorrow, it must mean that not even the Nazis could destroy his humanity. And this awareness, that he was still human, gave him hope and the will to continue.The article is worth reading also for the excellent photo of Alekhine later in his career.
Does the AVRO photograph prove Alekhine was not an antisemite "in his heart" (whether or not he wrote the infamous antisemitic articles)? Not necessarily. Foward also has another article about the other great antisemite in chess, Bobby Fischer. They argue the solution to the mystery of Fischer's rabid antisemitism coexisting with his friendship with many individual Jews is that for him "Jew" was just a name for "enemy". Being paranoid, anybody he suspected of having slighted him in the most trivial way instantly became an "enemy", and thus a "Jew", and thus part of the worldwide "Jewish conspiracy" against him.
Fischer's case is extreme, but we all know bigots who say 'some of my best friends are Jews' despite the fact that they despise Jews. They are not lying about their friendships; their mistake is to think this proves they are not bigots. It is possible that Alekhine's friendship with, and public praise of, Jewish players he knew were genuine, and that his belief that "Jewish chess" is a menace was equally honest. Jeremy Spinard's Anti-Semitism in Chess gives the example of Emil Diemer, of Blackmar-Diemer gambit fame, who was a Nazi party member and an antisemite, yet was a close friend of the Latvian Jew Nimzowitsch.
So Alekhine's defenders cannot use this "contradiction" as proof that he didn't mean what he say in his antisemitic articles. Does this condemn Alekhine? In my view, no.
1). First, if his friendship with Jewish players is no proof his antisemitic articles did not reflect his actual view, it of course does not prove his articles did reflect his views. That he might have believed what he wrote is no proof that he did.
2). Second, suppose it is conclusively proven -- say, by the discovery of a personal letter to a friend where Alekhine declares he hates "Jewish chess" -- that Alekhine meant what he said in those articles. If this were a contradiction with his friendhip with, and published praise of, Jewish players, we would be forced to conclude he was an enormous hypocrite, praising and being on friendly terms with many people he actually despised! This would be a worse condemnation of Alekhine's character than any belief, however foolish or mean-spirited, he held about the evils of "Jewish chess". But, I argue, it is quite possible that his friendship with Jewish players is genuine even if he was an antisemite about Jews "in general".