According to the theory of relativity, the statement that "each object is moving at the speed of light relative to each other" is not correct. The principle of relativity, as described by Albert Einstein, states that the laws of physics are the same in all inertial reference frames.
In the scenario you described, where two objects are moving in opposite directions at half the speed of light relative to an observer, we cannot simply add the velocities to determine their relative velocities. As objects approach the speed of light, relativistic effects come into play, and the simple addition of velocities no longer holds.
According to Einstein's theory of special relativity, the relative velocity of two objects moving in opposite directions cannot exceed the speed of light. As an object approaches the speed of light, its mass increases, and it requires more and more energy to accelerate it further. The combined effect of these relativistic phenomena prevents the relative velocity between the two objects from reaching or exceeding the speed of light.
Therefore, in the scenario you described, each object would be moving at a velocity less than the speed of light relative to each other.