I would say that the reasons run deeper than a power play.

Freemasonry demands active participation in a religious liturgy in which Christ is implicitly excluded.

When the Church warns against such worship and the basic attitudes (beliefs) it inevitably expresses, it is not expressing hatred but charity: concern for souls and loyalty to the mission it received from Christ in Mt 28:19-20. My guess is that you will find the same instincts in e.g. Eastern Orthodox churches.