J.R.R. Tolkien wrote more about the Noldor than the rest of the Eldar -- and quite a lot there was to write about them! Consequently, they also get quite a lot of attention from fanwriters. A lot of it is not very positive.
For all their manifold failings and multitudinous "dumb stunts", the Noldor are my favorite Quendi. Here are a few mini-essays defending and/or analyzing them.
The victims of the First Kinslaying were the Teleri of Alqualonde. The victims of the Second Kinslaying were the Sindar of Doriath. The victims of the Third Kinslaying were the people of Sirion, who were mostly refugees from Doriath and Gondolin, and so included both Sindar and Noldor, living as one people.
Most Noldor were not Kinslayers. In fact, a majority of the Noldor in Beleriand were probably dead by the time of the second Kinslaying, considering that it occurred only after both the Nirnaeth Arnediad and the sack of Nargothrond. Any Sinda who believes he or she has a grievance against all Noldor, or even all Exiles, because of the Second Kinslaying is coming from an emotionally understandable place, but not one that is rationally justified.
The "Calaquendi" are not more intelligent than the "Moriquendi". They have different skills due to different backgrounds, neither superior to the other. The Calaquendi are *not* "better" than the Moriquendi, nor are they "worse"; they are all products of their environments. Neither group is without major foibles and flaws, both groups have some severe embarrassments (sons of Feanor, Eol -- Maeglin was a joint effort). Both groups also have shining exemplars of heroism. But if you are going up against a servant of the Enemy with some kind of Power, you are better off with an Elda who has the light of Aman in his or her eyes. That's the difference -- that there is a difference.
Galadriel is not a typical Noldor, nor is she ethnocentric. Her mother was a Teler, her grandmother a Vanya, and she married a Sinda. She moved to Menegroth some time before she married Celeborn, to study with Melian the Maia. She could, in fact, be accused of "going native" quite quickly. When we see her in Lord of the Rings, she is the Lady of the Wood, integrated into and respected and loved by the community. There is no indication that anyone besides Oropher holds Galadriel's Noldor ancestry against her. It isn't an unreasonable thing to speculate, but there's no evidence for it, and she has spent nearly three ages living partly or mostly among Sindar and Nandor. The manner in which Galadriel is treated in some fanfics seems to me to be completely unacceptable.
Also, I do not get why people think Galadriel had close -- or any -- ties with any of the Sons of Feanor before the Second Kinslaying. (Assuming she was still in Beleriand at all.) Even in Valinor, she couldn't stand Feanor and opposed him even over trivial matters. Later, it was her mother's people who were slaughtered at Alqualonde, and she herself was one of those abandoned to traverse the Grinding Ice. A truce for one's people's sake is one thing, truly restored trust another. If that is not enough, consider that Celegorm and Curufin led a coup against her brother Finrod and sent him to his death beneath Tol-in-Gaurhoth. Galadriel may have been practical enough not to adopt Orodreth's stance of absolutely no contact with or support for the Sons of Feanor, under any circumstances, but this is not something to be lightly forgiven. I imagine there was no doubt that she wanted nothing to do with her half-cousins.
On a somewhat different subject, there is absolutely no mention in The Silmarillion of what Galadriel and Celeborn were doing between the revelation of the Kinslaying and Galadriel's refusal to sail West after the War of Wrath. In Lord of the Rings, Galadriel indicates she and Celeborn left Beleriand before things there got really dire. The Histories are somewhat vague on the issue, but it seems likely Galadriel and Celeborn spent the latter part of the First Age somewhere near Lake Evendim, east of the Blue Mountains, governing a settlement.
Between the Great Journey and the deaths of the Trees, there is theoretically no reason why the Sindar and Nandor left in Middle-Earth could not, once they had the shipbuilding technology, simply sail to Valinor on their own. There is however no indication that this happened, ever, even once. It may be that they just didn't want to.
During most of the First Age, Valinor was hidden and no one could sail west, until Earendil and Elwing managed with the Silmaril. This was presumably directed both at the rebellious Noldor and at Melkor & company.
At the end of the First Age, the Valar invited all the survivors to come to Valinor, offering pardon to the Noldor, possibly with the exceptions of some rebel leaders. At this point, there was a marked shortage of rebel leaders -- Fingolfin and all his children were dead; all the sons of Finarfin were dead; all but two of the sons of Feanor were dead; Idril had been a child at the Flight of the Noldor, and was missing anyway; Ereinion hadn't even been born at the time. This leaves us with Maedhros and Maglor, who would have been judged for crimes above and beyond rebellion, Galadriel, possibly Celebrimbor, and possibly some Rebel Leader No-Names. Maedhros killed himself and Maglor wanders alone, so the only possible rebel leaders to be denied pardon are Galadriel, possibly Celebrimbor (his age is never clearly established), and possibly Rebel Leader No-Names. Whether Galadriel was exiled, and if so whether she refused pardon or was denied it, changed quite a lot in Tolkien's various writings.
I hypothesize that those Noldor still Exiled were not forbidden from sailing West -- but from Valinor, from their homes. On Tol Eressea they might settle.
Ship traffic to and occasionally from Valinor and Tol Eressea was relatively open through the Second Age, although few ships sailed east, possibly none farther east than Numenor. All that came to an end, of course, with the Akallabeth. In the Third Age, in order to reach the West one had to find the Straight Road, and how this happened is not at all clear. (I'm also a bit curious about the sailors. Did they make round trips? Did Cirdan have this neverending supply of sailors? Did the sailing elves just have to learn how to handle the boat themselves? But that's another story.)
One of the most difficult things for a Noldor to say is, "I can't do this." They aren't stupid; surely they realize that crossing the Helcaraxe is going to be, er, hell, that getting into a duel of magic with a Maia can't go anywhere good, that stealing two Silmarils from Eonwe can only possibly go very very bad, that staying behind to defy "Annatar" isn't really going to help. Be it through overconfidence or courage or sheer bloodymindedness, the Noldor tend to try anyway -- and sometimes they do the impossible, and cross the Helcaraxe to arrive with the sounding of trumpets. The rest of the time -- they fall.
I think this Noldorin trait makes it all the more impressive that Galadriel refused the One Ring. She said, effectively, "I can't do this. I cannot turn this ring to good ends. This task is beyond me." Not for nothing is she numbered among the Wise.