After rewatching I like the ep a bit better.
Why is she blamed for the war - which she seems to accept - when we saw that nothing she did actually made a difference to either the battle starting, or to the outcome of that battle?
I understand more why Burnham blames herself for the war than why others might. From what I got from it, in addition to feeling guilty about the mutiny and not being able to save her captain, she blames herself for the war by ultimately failing in her attempt to stop it before it began (i.e. giving the Klingons a Vulcan Hello).
I'm right there with you on it being bullshit for everyone else to blame her for the war. The Klingons were very clearly the aggressors. They attacked Federation ships in Federation space. I don't understand how it's even an issue.
Burnham's plan was kind of goofy, though. Unless the Shenzhou could destroy the sarcophagus ship in one fell swoop, I'm not sure it would have really done anything to stop the war.
Come to think of it, if the show was really determined to blame her for starting a war with the Klingons, I think the better route would have been to let Burnham's mutiny succeed, but her plan ultimately fail. That is, let her get off the first shot, but have it do nothing to prevent the already-summoned Klingon fleet from pressing the attack. Then it really could be viewed as her fault.