The answer is no, we cannot rule out forces not directed along the line joining particles with current theory. As you point out, magnetic monopoles are a counterexample, and, as CuriousOne points out, magnetic monopoles both fit into a classical framework, are consistent with the Standard Model and are actively, experimentally sought.
Some historical comments on this question are in order though, I believe.
One reason that you might classically give (i.e. in Newtonian mechanics) for a "yes" answer to your question is that an assumption of acting of force along the line joining the two particles is needed, otherwise the system's angular momentum is not conserved. Consider two particles, equidistant from the origin and with equal and opposite forces on each other at right angles to the line joining them. The orbital angular momentum about the whole origin steadily and linearly increases with time! So in Newtonian, action-at-a-distance thinking, this is a problem. Hence, I believe Newton himself postulated that the force between particles is always along the line joining them. Notice that, contrary to some of the comments, this is not a breach of Newton's third law. A postulate of force along the line joining particles is something further to and independent from Newton's third law.
Another way of thinking about this from a Noether's Theorem standpoint is that our proposed, spontaneous angular momentum-generating system above has physics that are not invariant with respect to a global rotation of our co-ordinate system. You need to choose a preferred direction to define the force direction in our example. So our system's description is not rotationally invariant, hence the breakdown of the law of conservation of angular momentum.
A flaw in all of the above (assumption of force along the line joining particles) as we now know is that the World is not just particles and "empty space" (in the sense of a void). There are fields too, and these are strongly believed to have an objective reality in modern physics (indeed I would say that "empty space" is made of ground state quantum fields). Physics is local. So in tallying up angular momentum, we need to take account of the momentum and angular momentum of fields. Thus, in the classical sense Newton's third law does not hold, but its abstraction and generalisation to the law of conservation of momentum most certainly does when we tally up the field contribution. Likewise for angular momentum.
