I don't think it was as simple as him deciding he didn't hate Snape when he found out he was in love with Lily. I think it was a more gradual process, that started when he stumbled into Snape's memory in HBP, because that's when he started to understand why Snape hated his father, but it wasn't easy for him to see because you don't want to think that your father is that horrible. But it wasn't until he saw all of Snape's memories that Harry truly understood him and therefore accepted him and began to respect him.
he did because if you paid close attention in the 19 years later part in the hp7 then it says that harry named his son Albus Severus Potter "Albus Severus you were named for two headmasters of Hogwarts. One of them was a Slytherin."
I think Harry would feel close to what we felt. J.K. Rowling put us right with Harry in the series. I think there was some resentment at first and anger, but I bet reality set in quick and Harry accepted things as they were. And yes...he did name his child after him as well as Sirius. We all know how Harry felt about Sirius, so that has to say something about how he felt towards Snape.