McGonagall was a trusted ally of Dumbledore in the cause against Voldemort. With this in mind, did she know about the plans and actions of the Order of the Phoenix?
And did she know about
Snape’s role as a double agent?
At least, I expect she would, as she was certainly a member. When Harry and co are at Grimmauld Place, they witness members arriving at the house, and Professor McGonagall is among them:
The doorbell rang several times a day, which was the cue for Sirius’s mother to start shrieking again, and for Harry and the others to attempt to eavesdrop on the visitor, though they gleaned very little from the brief glimpses and snatches of conversation they were able to sneak before Mrs. Weasley recalled them to their tasks. […] Harry caught sight of his Transfiguration teacher Professor McGonagall, looking very odd in a Muggle dress and coat, and she also seemed too busy to linger.
— Order of the Phoenix, chapter 6 (The Noble and Most Ancient House of Black)
The notoriously dubious HP Wiki article about McGonagall states that she was also part of the Order in the First War, but I can’t find anything to back up this assertion. She doesn’t get listed as part of Moody’s photo of the original Order; on the other hand, she would certainly have been of-age during the First War, and teaching at Hogwarts. (In Umbridge’s inspection, she tells us that she’s been at Hogwarts for 39 years, well before the First War began.)
Dumbledore tells an entire courtroom of wizards that Snape defected in one of his Pensieve memories:
“No!” shouted Karkaroff, straining at the chains that bound him to the chair. “I assure you! Severus Snape is a Death Eater!”
Dumbledore had gotten to his feet.
“I have given evidence already on this matter,” he said calmly. “Severus Snape was indeed a Death Eater. However, he rejoined our side before Lord Voldemort’s downfall and turned spy for us, at great personal risk. He is now no more a Death Eater than I am.”
— Goblet of Fire, chapter 30 (The Pensieve)
If he’s willing to tell them, then I think McGonagall would know as well.
Voldemort would know that Snape had taken up a position at Hogwarts. The only way Snape does this and keeps his head is to pretend to be a double agent for Voldemort.
So even if she isn’t told explicitly, McGonagall is intelligent: she knows that Snape works for Dumbledore, and pretends to work for Voldemort, so he must be a double agent.
It’s very unlikely she knows why Snape defected, as Snape makes Dumbledore promise not to tell anyone the true reason. And she probably believed Snape really was a double agent on Voldemort’s side when he killed Dumbledore.
Though she might not have been during the first war against the Dark Lord, when the Order of the Phoenix reconvened after the Dark Lord’s return to corporeal form, she would have known the activities of the Order since she was a member herself. When Harry, who by then knows everyone in the Order, sees through the Dark Lord’s eyes that Nagini attacked Arthur Weasley, he is happy to see her because he knew he needed an Order member.
“Over here, Professor.’
Professor McGonagall came hurrying into the dormitory in her tartan dressing gown, her glasses perched lopsidedly on the bridge of her bony nose.
‘What is it, Potter? Where does it hurt?’
He had never been so pleased to see her; it was a member of the Order of the Phoenix he needed now, not someone fussing over him and prescribing useless potions.”
- Harry Potter and the Order of the Phoenix, Chapter 21 (The Eye of the Snake)
Therefore, Professor McGonagall was officially a member of the Order, not just an ally - so she’d know everything the other members did about Order-related plans.
Professor McGonagall knew that Snape was working with Dumbledore. Everyone in the Order did, which is why Snape was actually let into Order meetings - if they didn’t know, they’d likely have tried to not let him it. However, she didn’t know that Dumbledore and Snape planned Dumbledore’s death. When she found out Snape killed him, she was shocked.
“She stared at him for a moment, then swayed alarmingly; Madam Pomfrey, who seemed to have pulled herself together, ran forwards, conjuring a chair from thin air, which she pushed under McGonagall.
‘Snape,’ repeated McGonagall faintly, falling into the chair. ‘We all wondered … but he trusted … always … Snape … I can’t believe it …”
- Harry Potter and the Half-Blood Prince, Chapter 29 (The Phoenix Lament)
She knew Snape’s history, and that Dumbledore had a very good reason for trusting him, but she (like the rest of the Order) didn’t know exactly what that reason was.
“He always hinted that he had an iron-clad reason for trusting Snape,’ muttered Professor McGonagall, now dabbing at the corners of her leaking eyes with a tartan-edged handkerchief. ‘I mean … with Snape’s history … of course people were bound to wonder … but Dumbledore told me explicitly that Snape’s repentance was absolutely genuine … wouldn’t hear a word against him!”
- Harry Potter and the Half-Blood Prince, Chapter 29 (The Phoenix Lament)
She seemed to know what everyone else in the Order knew about Snape’s allegiances, but no more, since she’d stopped believing he was on their side after Dumbledore’s death.