I have a linear regression model that has no multicolinearity problem with low VIF scores. However, when I include the interaction term, this interaction term and its components get very high VIF scores. Can I ignore the multicolinearity problem and high VIF scores of the interaction term in this case?
The short answer is yes. Interaction terms tend to be collinear with the original variables involved. That is why post-hoc interaction tests are often underpowered.
Interaction that is unaccounted for renders the estimate wrong, while inflated variance inflates p-value. If the interaction terms are already statistically significant, inflation of variance is no longer a problem.