You would probably at least carry an ID no matter what...
You would probably have Ins. because it's crazy not to.
No you don't need a passport.
No you don't need a permit (mexican boating).
Yes you need a mexican fishing license.
And NO, the mexican Navy has no way of checking the authenticity of your proof of ins and vessel registration. As I understand it, they are not suppose to even board your vessel at all. But I could be dead wrong on at least one of the above.

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I would get a passport and carry it anyways because, what if???