After watching many streamers in a GTA V Roleplay, it helped me understand (but nowhere near to justify) why Sansa received the hate from the general GOT fandom.
In the GTA V Roleplay, you decide how many POVs to watch, so when you go back and forward from many, you already know who's gonna betray whom, and it can be kind of frustrating if your favorite streamer doesn't realize or doesn't make any decisions that puts in disadvantage the scheming plan. I've seen many viewers doing metagaming in order to help their favorite streamers but they don't realize these guys are doing a fiction, writing it live and, of course, they don't know what the others roleplayers are thinking or planning to do, nor is ethical for them to do metagaming.
In the books and in the series (specially talking about Book 1 and S1) we see every character POVs involved in the conspiracy to call out Joffrey an illegitimate king for not being Robert's real son, how the Lannister's try to deal with it, the Starks going to civil war and independence movement later on, wins and fails from both sides. When we go to Sansa's POV, she isn't in full knowledge about everything unwrapping; she was raised to believe kings, queens and princes are honorable people with good intentions; same with lords and ladies of great houses.
When Ned tried to leave King's Landing with her and Arya, Sansa failed to see the problem behind, nor Ned explained clearly how the world really is and the new circumstances. All Sansa dreamt of was to marry a prince, just like almost any other noble girl like her wanted, so she wanted to stay. Later on with Cersei, Sansa tried to help her father and explained that he was an honorable man with good intentions. After proving to her Ned committed treason against the crown, Sansa was promised that her father would receive a "minor" punishment if she cooperate with them, and she did, still with the idea of good queens being the only thing they can be. Even though Cersei manipulated her, she was convinced that sending Ned to the Night's Watch would be the end of all this part of the major problem.
We know how all it ended: with Joffrey ordering the execution of Ned, moved as well by the people of King's Landing, opening the way for civil war and The North fighting for independence; decisions with no point of reconsideration from the Starks.
The death of Ned was Sansa's fault? Absolutely not. To some degree, it was Ned's own fault for speaking out loud his plans to Cersei and Littlefinger, building the way for the ultimate responsible of his death: Joffrey. At that point, there was nothing for Sansa, even for Cersei to do, even if both tried to stop it.
Is Sansa guilty of not knowing the people around her? Of being naive? No, she was a child only trying to see the good in everyone, because she grew believing in an idealistic world of honorable men and women, where virtue would be the ultimate winner, and no one tried to explain her how things really work. She was mocked by Arya because of it. Ned and Catelyn stayed silent almost everytime she spoke her mind, and the rest used her to their convinience for their schemes.
Then why people still hate her? The main reason I find is that knowing all POVs, they expected Sansa to magically know what was going to happen and do the "right" thing. Wait, but Arya did see all of this! How Sansa couldn't? I give you that Arya was conscious of how the Lannisters really were at the moment they ordered to kill Lady for Nymeria's missing, and it helped her the fact that she was never really into kings and queens fairytales, so she didn't idealize nor trusted royalty as Sansa did. And even with Arya knowing all this, there wasn't much for her to do. But Sansa was a spoiled child, didn't you see it? That's why we hate her! Well, so was Arya and Jon, with them throwing tantrums when they didn't like something or were questioned of their ways of doing things. But they grew to be loved by fans, and mostly because their storylines grew apart from the political conflict; they grew as characters in a more magical context, meanwhile Sansa lived in the middle of the political one (no magical context at all) and used as a coin of exchange between Lannisters, Tyrells, Arryns and Boltons. Making a misstep would end on her death, so she more than ever had to stay under the light to survive if she wanted to go home.
Finally, she grow up and took everything she learned from the greatest schemers in the game, and outsmarted every single one of them, won the Battle of the Bastards, won The North back and supported Jon as king even when he was away, maintaining the order between northern houses, preparing for the winter and wars to come. Ultimately, after Jon's exile, she was chosen as Queen in The North, mantaining their independence just like Robb, Catelyn and Jon wished for.
So, don't blame Sansa for not seeing the bigger picture like you did as omnipresent viewers of this world building.
Update: Re-edited because I probably wrote this almost drunk, and english is my third language.
