As far as I know there's no mathematical or physical reason to outright forbid magnetic monopoles. On the contrary, there is a well-known argument by Dirac that says that if they would exist then charge is quantised, which we know it is. This is one of the reasons people are still looking for magnetic monopoles.
Div(B) = 0
And update it to say
Div(B) = sigma
Where sigma is a field describing the monopole density. Theres a ready "gap" in Gauss' law for magnetism where you can easily stick monopoles. Of course the divergence would be zero in the absence of monopoles, just as the divergence of the electric field is zero in the absence of electric monopoles, but decidedly non-zero when there's an electron around.
∇⋅E = ρ(electric) / ϵ0
∇⋅B = μ0 * ρ(magnetic)
∇⨯E = -μ0 * J(magnetic) - ∂B/∂t
∇⨯B = μ0 * J(electric) + (μ0)(ϵ0)(∂E/∂t)
We could switch every physics textbook to using the above today, and the only difference would be setting ρ(magnetic) and J(magnetic) to zero when there are no monopoles in the problem.
[0] Griffiths Introduction to Electrodynamics 3E, Section 7.3.4
> so close to zero that monopoles would be extraordinarily weak if they did exist
Why? I can't think of a reason why would this be the case? You are not solving Maxwell's equation for the universe. You can have divergence of electric field closed to zero because you have very low density (the field source) in the region you are studying.
So no, it was not explicitly ruled out by Maxwell's equations. It is not even ruled out because we did not explore the full phase space. And it depends on which monopole you are talking about (Dirac monopole, GUT monopole or EW monopole).
