Because Walton sees his own thirst for knowledge in Victor (the stranger), he responds to him with unabandoned enthusiasm. He almost seems to worship Victor as he talks to him more and more on the ship.
Shelley foreshadows this type of response from Walton when he writes his sister and tells her how much he longs for an intellectual friend. He recognizes Victor as the answer to his desire almost immediately.
Because Walton is a Romantic, he disregards all danger connected to Victor. He allows a very ill stranger who is chasing a monstrous like creature across a barren wilderness to come aboard his ship and be treated better than his crew. He cares only about feeding his quest for knowledge and satisfying his imagination.