In the beginning, Snape changed side because of his love for Lily and to protect Harry. But after that, he actually changed side and did right thing not only for Lily.
1/In DH, chapter 33 In Harry's sixth year, Snape learned the truth that Harry is a Horcux and need to die anyway (for the greater good). So, his many years protect Harry is in vain. But his not abandon light side, still continue for support order of Pheonix, kills Dumbledore in his order, become a murderer, continue protect Hogwarts students, help Harry destroy Horcux.
Snape's father is a muggle, he grew up in muggle world, so Snape has muggle's ID card and passport, he can fake he is dead (he is a potion master and dark art master), and dump the light side, go to other country and live as a muggle. But he didn't do that.
2/And in DH, chapter battle of 7 Potters, Snape protected George/Lupin, tried to stop DE hitting them, even he don't have to.
3/ He obviously cared for McGonagall, he had been quite happy when she returned from St Mungo (book 5, chap 38)
And in Battle of Hogwarts, he only defended himself, he not attacked Macgonagall when she tried to kill him.
4/He protected students when he was headmaster: for example: He gave Neville, Ginny (and Luna) detention with Hagrid instead of subjecting them to the Carrow's torture (book 7)
about strict toward students, not only Snape but also Macgonagall is same. She deducted 50 points/1 student in Harry's first year only because they out of bed after curfew. And she let Neville stay outside, although she knew that a murderer is in outside.
5/In book 5, when Snape knew that Sirus is in danger at the ministry, he contacted the order to save Sirius.
6/ He cared for Narcissa so much that he accepted to be killed if he failed to protect her son. He cared for Draco
7/ He cared enough for Harry, Ron and Hermione to tried to save them from Lupin in book 3.
8/Snape always give Harry, Ron and Hermione high mark they derserve.
9/In book 6 (HBP) when Harry nearly killed Draco, when Snape heard screams in the hallways, a yell of "murder" from Moaning Myrtle in her bathroom, or was called on or needed to assist any student, did he think first that he would not go if it was a Gryffindor? No. He ran immediately every single time and didn't care who is the victim.
10/He was clutching a chair and looking pale in the face at the thought of Ginny Weasley being taken into the Chamber of Secrets (book 2, Chamber of secret)
11/ He refused to tell Voldemort who the owner of the elder wand was and how he spent his last moments while suffocating to death making sure that Harry had the information that he needed to complete his mission.