Guy 1: She don't think we should see each other anymore.
Guy 2: Well, maybe it's for the best.
Guy 1: I don't see it.
Is "I don't see it." natural here to mean "I don't agree."?
Guy 1: She don't think we should see each other anymore.
Guy 2: Well, maybe it's for the best.
Guy 1: I don't see it.
Is "I don't see it." natural here to mean "I don't agree."?
No, I don't think that is really natural. Saying "I don't see it" basically means that you (literally) don't see something, or you aren't perceiving what somebody else is (e.g. you don't understand something, or you see no evidence of what they're talking about).
You can, however, express disagreement by saying you don't see something in the same way:
I don't see it that way.
or
I don't see it like that.
Note that this generally has a sense of "I think you're right about the facts, but I have a different opinion about what they mean", not "I think you're wrong about the facts".