Is using the word Eskimo in Eskimo Curlews considered racist?

No more than using the Word German in German Measles. Eskimos do not call themselves Eskimos to be sure (they call themselves Inuit), but the Word "Eskimo" was not at any time an insult towards this group of people. If you are so hypersensitive that you think it is racist to describe a group by any other term than the one they use for themselves, then you must also find the Word "German" racist, since Germans call themselves "Deutsch".

In any case, we are not talking about the people here, but a bird. You would have to be hypersensitive to the point of insanity to consider that usage racist. (There are people this crazy, however)