On the other hand (debates about the unity of the trinity aside), Christians believe in a single God as well (and that God is understood by Muslims to be Allah)

On the other hand (debates about the unity of the trinity aside), Christians believe in a single God as well (and that God is understood by Muslims to be Allah). So while the shahada is strongly associated with Islam, I doubt it would particularly conflict with Orthodox Christian teachings (IANA religious scholar). So perhaps the better analogy would be the US president wearing "A Mari Usque Ad Mare", the Canadian motto, which means "From Sea to Sea".