Though Price seems to exalt "reason" and "nature" he still sees the Bible as the Word of God and believes Jesus as Messiah and in the miracles and prophesies contained therein. Still Price's sentiments conflict with historic orthodox Christianity. In his first Sermon "Of the Security of a Virtuous Course," Price makes a very works-like argument for salvation that would undoubtedly trouble the orthodox:
Christianity informs us, that good men will be raised from death to enjoy a glorious immortality, through that Saviour of the world, who tasted death for every man.
Doesn't orthodox Christianity teach that no man is good (but one)?
Price finds the notion of eternal damnation so disturbing that he hedges on its truth. But he's clear that you avoid the possibility by practicing virtue, and you risk it by practicing wickedness. As he notes:
To act righteously is to act like God. It is to promote the order of his creation....It must, therefore, be the likeliest way to arrive at happiness, and to guard against misery under his government....The Christian religion confirms this expectation in a manner the most awful, by teaching us that the wicked shall be turned into hell, with all that forget God; that they mall be excluded from the society of wise and good beings; and punished with everlasting destruction from the presence of the Lord and the glory of his payer. It is, at least, possible this may be the truth. The arguments for a righteous government in nature, and for the truth of Christianity, have, at least, force enough to prove that it is not certain but that wickedness will produce the greatest losses and evils in another world; and that, consequently, there is a real and inconceivable danger attending it....
In a later sermon, Price makes an argument for the "essentials" of Christianity that almost perfectly parallels what John Locke taught in "The Reasonableness of Christianity." Basically he draws a lowest common denominator among Socinianism, Arianism, and Trinitarianism [Keep Locke, who influenced Price, in mind when you read this. To Trinitarians, the doctrine is central to Christianity. If one draws essentials of Christianity and leaves out the Trinity, then it's entirely reasonable to assume one is not a Trinitarian as Locke's critics did]:
And my chief intention, in the present discourse, is to attempt this, by shewing you, that Christians, of all parties, however they may censure one another, and whatever opposition there may seem to be in their sentiments, are agreed in all that is essential to Christianity....
In attempting this, I will recite to you those doctrines and facts of Christianity which all Christians believe, and which are so plainly revealed as to exclude the possibility of disputes about them....
In the first place; the Gospel teaches us that there is only one living and true God. This is a fundamental doctrine which the New Testament holds forth to us in almost every page. There is but one being good, says Jesus Christ, that is GOD. There are, says St. Paul, 'Gods many; but to us there is but one God, the Father....
But farther; the Gospel teaches us, with perfect clearness, that this one God is possessed of all possible perfection; that he is infinitely wife, powerful, righteous, and benevolent; that he is the moral Governor of the world, an enemy to all wickedness, and a friend to all goodness; and that he directs all events by his Providence so particularly as that the hairs of our heads are all numbered, and that a sparrow does not fall to the ground without him. It teaches us also to imitate, to serve, and to worship him, and to put our trust in him; and comprehends the whole of our duty in loving him with all our hearts, and in loving our neighbour as ourselves. It declares to us the necessity of repentance and a holy life; a future state of rewards and punishments; and a future period of universal retribution when all mankind mall be judged according to their works.
There are no doubts about any of these particulars among Christians; and they include all that it is most necessary for us to know. But the doctrines which most properly constitute the Gospel are those which relate to Jesus Christ and his mediation. Here, also, there is an agreement with respect to all that can be deemed essential; for there is no sect of Christians who do not believe that Christ was sent of God; that he is the true Messiah; that he worked miracles, and suffered, and died, and rose again from the dead, as related in the four Gospels; that after his resurrection he ascended to heaven, and became possessed of universal dominion, being made head over all things in this world ; and that he will hereafter make a second appearance on this earth, and come from heaven to raise all mankind from death, to judge the world in righteousness, to bestow eternal life on the truly virtuous, and to punish the workers of iniquity.
Now, this is all quite biblical and perhaps qualifies as "Christianity." Yet, upon reading Price's sentiments, traditional Christians might mistakenly impute belief in orthodox Trinitarian doctrines to Price as they have done with Locke and other Founding Founders who identify as "Christians" or otherwise praise "Christianity" in their quotations.
Price, remarkably liberal for his time and today, goes on to identify who it is that qualifies as "Christian" under his aforementioned "essentials":
These are the grand facts of Christianity, which Calvinists and Arminians, Trinitarians and Unitarians, Papists and Protestants, Churchmen and Dissenters all equally believe. More especially ; with respect to the purpose of Christ's mission, we all equally hold that he came to call sinners to repentance, to teach us the knowledge of God and our duty, to save us from sin and death, and to publish a covenant of grace, by which all sincere penitents and good men are assured of favour and complete happiness in his future everlasting kingdom.
The latitudinarian notion that Trinitarians, Unitarians and Roman Catholics are all true Christians remains disputed in Christian circles.
Price later explains the differences among Trinitarianism, Socinianism and Arianism and argues for Arianism as the rational and correct understanding of Christianity. This passage on the nature of Jesus Christ perfectly exemplifies Price's "liberal" Christian views that saw Jesus as Messiah and included Socinianism, Arianism and Trinitarianism within the ambit of "Christianity" while criticizing those views with which he disagreed:
Give me but this single truth, that ETERNAL LIFE is the gift of God through Jesus Christ our Lord and Saviour and I shall be perfectly easy with respect to the contrary opinions which are entertained about the dignity of Christ; about his nature, person, and offices; and the manner in which he saves us. Call him, if you please, simply a man endowed with extraordinary powers; or call him a superangelic being, who appeared in human nature for the purpose of accomplishing our salvation; or say (if you can admit a thought so shockingly absurd) that it was the second of three coequal persons in the Godhead, forming one person, with a human soul, that came down from heaven, and suffered and died on the cross: Say that he saves us merely by being a messenger from God to reveal to us eternal life, and to confer it upon us; or say, on the contrary, that he not only reveals to us eternal life, and confers it upon us, but has obtained it for us by offering himself a propitiatory sacrifice on the cross, and making satisfaction to the justice of the Deity for our sins: I shall think such differences of little moment, provided the fact is allowed, that Christ did rise from the dead, and will raise us from the dead; and that all righteous penitents will, through God's grace in him, be accepted and made happy forever.
Note how Price referred to the doctrine of the Trinity as "shockingly absurd" while conceding that Trinitarians are nonetheless genuine Christians. The Trinitarians of his day, and many today do not return Price's favor by considering his Arianism, biblical as it were, "Christian." Rather, such was settled in orthodox Christendom as a soul damning heresy in 325AD. And, today, the orthodox still hold to those standards set out in the Nicene Creed.
Yet, Price's theology and that of other liberal, enlightened Founding era theologians (Priestley, et al.) profoundly influenced the American Founding. Thus when one confronts a quotation from a Founding Father talking up "Christianity," don't assume it necessarily meant "orthodox Trinitarianism." The Founder just as well could be referring to Price's or Priestley's uber-latitudinarian "rational Christianity," whose status as "real Christianity" was disputed then and remains disputed today.