“I have therefore thought fit to recommend, and I do hereby recommend, that Wednesday, the 9th day of May next, be observed throughout the United States as a day of solemn humiliation, fasting, and prayer; that the citizens of these States, abstaining on that day from their customary worldly occupations, offer their devout addresses to the Father of Mercies agreeably to those forms or methods which they have severally adopted as the most suitable and becoming; that all religious congregations do, with the deepest humility, acknowledge before God the manifold sins and transgressions with which we are justly chargeable as individuals and as a nation, beseeching Him at the same time, of His infinite grace, through the Redeemer of the World, freely to remit all our offenses, and to incline us by His Holy Spirit to that sincere repentance and reformation which may afford us reason to hope for his inestimable favor and heavenly benediction…”

Bold face mine. As we see, the Father is in there, Jesus is still the “Redeemer,” and the existence of the Holy Spirit is acknowledged, not denied.
Most people, whether in 1798 or in 2011, would see President Adams’ proclamation as explicitly “Christian.” What John Adams believed in private is of some interest, but of little importance. These days, we use the term “Judeo-Christian” to dispose of the question of whether Jesus is God or not anyway. And as we see here, in public, John Adams comes off more Christian than that, not less.