Yes, it is a Christian view. I think it is a misnomer to believe that Christian forgiveness somehow means there are no consequences for actions. Didn't Jesus forgive the sinner on the cross? The sinner was forgiven, and yet still died. The scripture says, "the wages sin pays in death" - that is the consequence. And yet, God resurrects and forgives.
maybe the confusion here is the word consequence - it could easily be replaced with "result". Your actions create results. Those results are independent of anyone's forgiveness of the harm your actions caused.
It could be something simple like - I tell my friend something in confidence. They don't keep it. I'm hurt, but I forgive them and we stay friends. The consequence is that I do not tell them confidential information. If it was a repeated pattern or something else very serious, then maybe I choose not to be friends with them any longer. That does not mean I don't forgive them.