I think it is unfortunate that the word "Decision Theory" is used for both VNM and CDT. These are not in the same reference class and are not inconsistent with each other. I think the distinction between CDT and EDT is orthogonal to whether we represent the utilities of the outcomes with a VNM utility function.

CDT says we should make our choice based on the distribution of outcomes if we intervene such that a is chosen. This is in contrast to EDT, which allows you to choose based on the distribution of outcomes in people who were historically observed to choose a. EDT is subject to confounding, therefore quite clearly, Gibbard, Harper and Lewis were correct to argue that CDT is superior to EDT. This is accepted in all academic fields, it is very reasonable to claim that CDT is the standard academic decision theory.

CDT tells you to compare your beliefs about the distribution of Y| do(a) to Y| do(a') whereas EDT tells you to compare your beliefs about the distribution of Y|a to Y|a'. Note that neither CDT nor EDT specify how to evaluate which distribution of outcomes is better. This is what you need VNM for. You could in principle use VNM for either, but I find it obvious that Von Neumann and Morgenstern were implicitly assuming a Causal Decision Theory.