>> she made a controversial theological statement... that Muslims and Christians worship the same God
That’s not controversial — it’s simply WRONG.
A Muslim can get through "I believe in One God" before stumbling over "the Father Almighty" since Islam provides no basis for regarding God as Father, then agree again with "maker of heaven and earth and of all things visible and invisible", then will deny the rest of the Nicene Creed.
A Christian can agree that "there is no god but God" (ignoring the Mohammedan conceit that the Arabic word for God is the proper name of the One Existing God and translating all the words of the first clause of the Shahada into English and taking the words at face value), but necessarily denies that Mohammed is God's prophet (or messenger or apostle, both of which are probably better tranlations of the Arabic rasūlu).
And if one goes beyond the respective creeds and into their elaboration, the disagreements in the understanding of God become deeper -- Muslims understand the first clause of the Shahada as explicitly denying the doctrine of the Trinity and the Sonship of Jesus.