[Spoilers Main] Why does everyone think Ned Stark is so honourable despite Jon?

I’m not saying they have to think he’s Jamie Lannister’s northern counterpart, lots of noblemen have bastards.

However, I’d expect his reputation for being unusually, notably honourable to be damaged by the fact that as far as the seven kingdoms now, he cheated on his wife less than a year after they were married and then proceeded to raise Jon, the human reminder of the stain on his honour, publicly in Winterfell where his wife and trueborn children reside and everyone can see him. Even Bobby B, who is shamelessly, publicly unfaithful to his wife doesn’t raise his bastards in the Red Keep.