Well, I don't agree. First of all, they did NOT know him. Grand Duchess Olga knew him. Alexandra and Nicholas did not know him. They took their time, in the middle of a war which had produced hundred of thousands of invalids, widows, orphans, refugees... to attend the petition of one man who was Jewish. I think that these "little" things (I suppose that for the wounded man was not so little thing) show where one stands. It is certainly not what could be expected from a Jew hater.
I'm not sure why you're fixating on Nicholas and Alix, since the imperial family consisted of more than just them, but I'll go along with this. They didn't need to know him directly--Grand Duchess Olga knew him and could vouch for him. He had a name and known history and was therefore removed from the larger, more abstract group of people known as "the Jews." That is why they may have felt more inclined to help him. And does petitioning for one man somehow compensate for the thousands of Jews that died in pogroms or suffered due to both longstanding and newly-instituted laws? When you're the most powerful couple in the Empire, capable of instituting major change and improving people's lives on a grand scale, the "little" things as you call them hardly matter. Not to mention that this was during the war, when they needed all of the good, loyal soldiers they could get.
Secondly, I do not think that this has to be considered an exception. Empress Alexandra in that letter is making the case for fairer treatment for the Jews of the Russian Empire: "here it is difficult for a Jew who is always hampered by legislative restrictions", "one would like him to be justly treated and not different to the others". When she writes: "The bad ones can be severely punished", I think that she means that there are two kind of Jews: "bad Jews" - revolutionaries and "good Jews" - the rest. Whereas "bad Jews" should be punished, the good ones deserved to be treated "not different to the others."
And therein lies the anti-Semitism--there are no "good Jews" and "bad Jews." There are
good people and
bad people. The religion has nothing to do with it. If you cannot make out the difference, then that tells me all I need to know.
On February 14 1917, just two weeks before the Revolution, Sandro (Grand Duke Alexander Mikhailovich, Nicholas' brother-in-law) wrote in a letter to his brother Nikolai Mikhailovich about a conversation with Nicholas and Alexandra:
"In my conversation with A and N, I also touched on two subjects, which have been raised by Protopopov [Minister of Interior, Empress Alexandra's protégé], the expropiation of landowners' land in favour of the peasants and equal rights for the Jews. It´s typical that Alix did not voice any protest on these questions, while he objected to the first and then appeared confused about the second, replying that it was equality only in the sense of widening the Pale of Settlement; I protested as strongly as I could, saying that concessions or new rights for the Jews were unthinkable, that we could not afford to be merciful to a race the Russian people hate even more now because of their negative attitude towards the war and outright treason; it was noticeable that Alix didn't protest, obviously such projects do exist."
Andrei Maylunas and Sergei Mironenko, A Lifelong Passion: Nicholas and Alexandra, p.532
Let's examine this more closely, shall we?
This is Nicholas' reaction:
"while he objected to the first and then appeared confused about the second, replying that it was equality only in the sense of widening the Pale of Settlement."
So basically his interpretation of "equality" is expanding the giant ghetto the Jews were forced to live in. A real advocate for Jewish rights there.
This is Sandro's reaction:
"I protested as strongly as I could, saying that concessions or new rights for the Jews were unthinkable, that we could not afford to be merciful to a race the Russian people hate even more now because of their negative attitude towards the war and outright treason."
I think that speaks for itself.
As for Alix? Not protesting is not the same thing as advocating.