Uhhuh.
Which is why they hate each other so much, actively try to kill one another and don't visit each other between adventures to play chess.
Obviously they are NOT seriously trying to eliminate one another, they are just arguing over procedures. They are shown to be friends and confidants throughout all three movies and would obviously prefer to look the other way to what each other is doing.
Remember that in movie #1, Xavier runs into Magneto and has a clear chance to just enter his mind and find out what's going on. But he doesn't do that. They have a nice little chat.
In movies one and two they're shown playing chess and having casual conversations.
They are not enemies, they're friends, and clearly view the whole "building bridges between human and mutant" or "mutants should rule the Earth" as a political debate. Each thinks the other will someday see it his way so there's no need for them to kill one another.
Chuck