Rushdoony made it clear in his book on the Church Councils that you could only worship Christ’s “divine nature.” Jay has pointed out where Rushdoony disagreed with Cyril (though the former didn’t realize it). I am going to point out where he disagreed with Athanasius.
One of the problems in saying “you only worship Christ’ divine nature” is that it assumes the hypostasis is constituted and theoretically separable. The post-Cyrilline church (which includes Chalcedon) rejected this as a Nestorian assumption. Jay has provided the quotes from Cyril on this point. I will mention Athanasius.
And we neither divide the body, being such, from the Word, and worship it by itself , nor when we wish to worship the Word do we set Him far apart from the Flesh, but knowing, as we said above, that ‘the Word was made flesh,’ we recognise Him as God also, after having come in the flesh. Who, accordingly, is so senseless as to say to the Lord: ‘Leave the Body that I may worship You;’ or so impious as to join the senseless Jews in saying, on account of the Body, ‘Why do You, being a man, make Yourself God John 10:33? (Letter 60.3)
And surely if the Flesh is inseparable from the Word, does it not follow that these men must either lay aside their error, and for the future worship the Father in the name of our Lord Jesus Christ, or, if they do not worship or serve the Word Who came in the Flesh, be cast out on all sides, and count no longer as Christians but either as heathens, or among the Jews. (Letter 60.5)
I don’t want to unnecessarily criticize Rushdoony. He was a hero and a giant among American Christians who truly saw the rise of the Power State. When he first warned of the coming American totalitarianism, the Reformed laughed at him (I also remember when I posted on Puritanboard of similar results, I was ridiculed; evidently, Bush’s trampling of the Constitution is okay, but when Obama does the same thing it is suddenly “bad.”). When the Calvinist seminaries were resting on their laurels after writing Yet a New Book on the Five Points Covering the Same Ground as the Other Books, Rushdoony was appearing in court testifying on behalf of homeschoolers, so that they wouldn’t go to jail.
Likewise, Rushdoony’s study habits inspire awe and continually goad me to redeem the time. Further, in the same book as above, while Rushdoony ultimately botches the 7th Ecumenical Council, he does make a good argument for images of Christ: an Incarnation that cannot be demonstrated is a contradiction in terms.
Sadly, that doesn’t redeem the book and numerous problems like the above keep one from recommending it.