Pride could’ve spied on the Elric Brothers while they were in Central, and Envy saw firsthand that Ed was apprehensive about fighting the 'people' on his monstrous form and using the Philosopher's Stone, which should have proven to him that Ed probably didn't have the mind to commit mass murder. Even if this somehow wasn't ever some kind of gossip in the military, one of the other homunculi should've known this about Ed.Kimblee doesn't know Ed (and therefore couldn’t really be trusted to judge his character himself), but I'm sure that word would have gotten around within the military that Ed doesn't like to kill people and actively tries to avoid it, enough so that someone like King Bradley might come to know that he wouldn’t make much of a killer.In Episode 37, Kimblee tells Edward about the plan to kill everyone in Briggs as part of the nationwide transmutation circle and that the higher ups in the military want Ed to be the one to carry this out.And with one right in front of him, he obviously goes for the kill. He wasn't targeting Ed, he was just walking down the street when he heard some call the name of a state alchemist. He's no more discerning than that, he even agrees to let Al go because Al's not a state alchemist.

Scar wants to kill all state alchemists for a combination of seeing their alchemy as blasphemous and blaming them for the massacre of his people.From Scar's perspective, if you join an organization, aren't you just as bad as someone who was a part of it at the time? By joining an organization, you're by-default okay with their record.Plus, after the first time, it's more a case of the Elrics having a particular grudge against Scar than the other way around.So why does he hold such a grudge against Edward and Alphonse? He can even go after King Bradley (it would end miserably, but Scar has no right to know how badass Wrath really is). Meanwhile Roy Mustang is lonely walking through rain, Kimblee is sitting immobilized in his cell and god knows how many Amerstris soldiers are on vacation or something like that. Why is Scar trying to kill Elric brothers two times? He sure hates state alchemists, but those two didn't do anything.

Truth full metal alchemist tattoo