How do energy changes in reactions avoid violating the conservation of momentum? As mentioned in this question, the idea of chemical potential energy explains how the thermal/kinetic energy of particles can change in a reaction; energy is taken in / released by the bonds broken / formed.

However, consider the reaction A -> B + C occurring in a closed system of just these single particles.
A reaction such as this is often endothermic. Therefore, the kinetic energy of the products must decrease. However, it is impossible to remove kinetic energy from the system without changing momentum (unless B and C are travelling in opposing directions to begin with, which is not the case. If they split in opposite directions, that will have already resulted in a KE gain).

How can this happen without violating the principle of conservation of momentum?

EDIT: Here is an explanation showing that it does not work if B and C travel in opposite directions:
How do you measure temperature? The thermometer has to be in thermal equilibrium, so you need to send the thermometer with the object. But that means that temperature, for our purposes, is going to be invariant between different reference frames. No matter how you're moving, the reading on the thermometer is the same.

This is clearly not the case with translational kinetic energy of the bulk material. In the rest frame of the object moving with constant velocity, the kinetic energy is zero.

Therefore, you should not mix up the thermal kinetic energy of the system with the translational kinetic energy of the system. They can't be the same thing. In other words, when the exothermic system loses energy, you don't get to subtract that from the translational kinetic energy.

See also these discussions: here and here.

I would also like to point out that you've just described a rocket. And rocket science, while complicated, is still obeying conservation of energy and momentum.