******Possible Spoilers from A World of Ice and Fire**********
1.) Underestimated how much influence Varys had with Aerys II. He really helped fukk up a lot of shyt.
2.) Varys when he killed Kevan Lannister on the show claimed he did things to protect the realm.
3.) Baelish is opposed to Varys. Littlefinger also was still in love with Cat Stark (get ready for some Harry Potter ish)
Putting that together I think Varys isn't saving the realm, he's interested in maintaining Aerys II's chaotic reign for some other reason. Maybe to weaken Westeros so that Pentos has more influence or something. Varys didn't seem too concerned with Roberts death obviously, but if he wanted peace keeping Robert alive was the best way. I highly doubt Robert really got killed by a boar accidentally. Also it's mentioned that Varys was one of the chief whisperer's in The Mad King's ear about Rhaegar wanting to betray him. This just caused more turmoil in the realm and led to Rhaegar and Aerys falling out. Varys isn't there for peace, he's there for something else. He is the real threat to Westeros, the actual "bad guy".
In addition I think fans generally see Baelish as a bad guy but he's really the "good" guy, just doing shyt in an ends justify the means way. He's not interested in saving the realm per se, he's interested in breaking the power of Lords that have screwed the realm and him over ( I might have to get into more stuff from the AWOIAF book to explain this further). Remember Baelish is a low class noble that scrounged his way up from shytty holdings and sees how Lords treat the people. I think this is why he loved Cat so much because she pretty much didn't shyt on him. Kinda like Lilly Potter did to Snape in the Harry Potter books. Hence Baelish is the anti-hero that we just don't notice. He seems to be against the "protagonists" (Starks) but he's really going to help them out in the end. Just like Snape saved Harry out of love for Lilly, Baelish is gonna help Sansa win back the North because of love for Cat.
