What is the exact reason that compounds such as carbon dioxide cannot interact with other compounds through dipole-dipole interactions? Whilst I understand that $\ce{CO2}$ has a linear structure, resulting in a vector sum of the dipoles of 0, I do not understand why the dipoles formed at the two oxygen atoms as a result of their increased electronegativity cannot interact with other molecules via dipole-dipole forces. Do the vectors equaling 0 somehow negate the present dipoles?
As the other answers have indicated, CO2 has no NET dipole moment. However it does have two dipoles pointed in opposite directions (as OP keeps mentioning). This means that CO2 can possibly interact through higher moments, such as the quadrupole moment. The mathematical procedure behind this is known as the multipole expansion. It is important to note however, the higher order multipoles get weaker and weaker by a factor of 1/R approximately, so quadrupole interactions are usually ignored for example.