The way I read it is that the "heal" part puts the character being healed into your territory where it comes under the protection of Altar of Dagon. Since Altar of Dagon is constantly active, it is constantly updating what characters it protects. Since the character is now in territory, the convert ability can't target the character.
Is this similar to the Belshazzar's Banquet + Iron Pan ruling? Or was that different because Iron Pan had a "condition" that was constantly updating? Because Altar of Dagon defaults to play and is a protect ability, doesn't it technically have the constantly updating condition, "If an Evil Character is in play, it is protected from conversion."?
If it is similar to BB + Iron Pan, I don't see how it could be ruled that it converts. If it is not similar to BB + Iron Pan, I'd like to know what is different.