Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system of two point particles in equilibrium with each other upon which a constraint acts so that the reaction forces are directed in a direction that is not collinear. Is such a situation possible?
If the forces are not precisely opposite one another, this would imply that conservation of (linear) momentum no longer holds; this has never been found in any experiment or observation.
Interestingly, the force must also point along the vector joining the two bodies: in other words, the cross product of the force with the position vector joining the two bodies at the point where the force acts, must be zero. If not, this would imply that conservation of angular momentum no longer holds. This, too, has never been found in any experiment or observation.
That's not to say it's impossible, or that designing experiments to look for it, in ways that are more sensitive than any yet done, are not worthwhile. We actually need people checking on this, to see if conservation of angular or linear momentum is all right, or just "mostly" right.