1) How can they want immortality, but dislike immortals?
2)If they dislike immortals then shouldn't they thereby dislike gods? i.e. the Raven Queen too?
Reading over the document, the only mention of Shadar-Kai hating immortals is in the text of the Paragon Path. It makes numerous mention of their service to the Raven Queen, part of whose dogma is to make sure that fate catches up to those who manage to cheat or defy fate. Usually this is reserved for undead who do not serve the Raven Queen directly, but could also be interpreted to be those who outlive or defy fate through magic, luck, will or divine providence.
Of course, if one of these people is Shadar Kai, and Shadar Kai serve the Raven Queen, who is the goddess of Fate, would that not mean that the Shadar Kai in question was fated to become immortal.
tl;dr: you can't argue with a zealot. If they achieve immortality, it is god's will. If others do, they are defying their god's will. Simple as that.
P.S. it is also possible that the fluff and Paragon Path were written by different people, which would explain the inconsistency. The first decided to change the Shadar Kai racial outlook, and the second did not get the memo.