Strongbow's conviction isn't "unshakable" because he has bent to Cutter's "new ways" and learned to adapt to them. It just took him longer than the others in the tribe to give in. His conviction is very strong, and a person's willingness to stick to their beliefs, despite what the rest of the world is trying to force upon them, is very attractive (to me at least).
That sort of faithfulness to tradition is what has kept a lot of cultures from dying out, such as the Irish who refused to give up their native Gaelic (I'm pretty such it's Gaelic) despite their leaders telling them to. It's that loyalty that Cutter valued so greatly during the Troll War, where he outright asked Strongbow and Moonshade to remind the tribe what it meant to be Wolfriders (I believe Strongbow and Moonshade are reference as the Keepers of the Way) when this was all over so that they didn't become like the Go-Backs and simply start enjoying the killing.