Essentially, Joe, you are offering an ipse dixit
argument, by referring back to your personal definition in responding to the issue of Arianism. However, i will accept the authority of the Catholic Encyclopedia:
A heresy which arose in the fourth century, and denied the Divinity of Jesus Christ.
Really, it's just laughable to cite the Catholic
Encyclopedia definition of "Arianism" as proof that the Arians were heretics who didn't believe in the divinity of Jesus. The Catholic church has its own definition of what it means for Christ to be "divine," and the Arians didn't share that particular belief. That doesn't mean, however, that the Arians thought that Christ wasn't divine, it just means that the Arians didn't think Christ was divine in the same way that Catholics think that Christ was divine. In particular, Catholics believe that Christ is cosubstantial with god, whereas the Arians, as far as we can tell, thought that Christ was "begotten" of god and, therefore, not
You conclude that Arians weren't Christians because they didn't believe in the Catholic version of Christ, but then accepting the Catholic position on Christ's divinity is merely begging the question. You're assuming that the Catholic church is right on this point. In contrast, I have no reason to think that the Catholic church has a monopoly on defining what it takes for Christ to be "divine."
As for what would distinguish a Presbyterian from a Muslim (and leaving aside all the delicious absurdities of John Calvin), i refer you again to the three descriptions extracted from the two definitions i quoted and linked (and resolutely ignoring your irrelevant remarks about the theological authority of the American Heritage Dictionary, whose claim cannot reasonably be considered to be less than your own personal claim). So long as a Muslim or a Bahai is not necessarily conscientiously attempting to live their life in accordance with the teaching of Jesus, following a religion based upon the teaching of Jesus, or professing a belief in the teaching of Jesus, they would not be Christians. That you or anyone else would choose to or choose not to so describe them has no meaning to me.
Dictionaries define word usages, they don't get into doctrinal debates. If people use the word "Christian" loosely, without regard to its theological dimensions, that's of little concern to the good folks at Merriam-Webster. That's why dictionary definitions are of very little use in theological discussions.
Definitions, in any event, follow usage rather than the other way around. We know that something, for instance, is a "dog" because we have examples of dogs that we can say, without question, are members of that category. So if some unknown beast comes to our attention, we can determine whether it fits into the definition of "dog" by looking at other examples that we're sure already fit that definition. In the same way, we don't define "Christian" in a vacuum, but rather by looking at examples that we're sure already fit that definition.
Someone who merely follows the precepts of Jesus, without accepting his divinity, is probably on the fringes of what we would consider to be the definition of "Christian." There's very little to distinguish someone who says "I follow the 'golden rule' laid down by Jesus, but I don't accept that he was divine" with someone who says "I follow the 'golden rule' because it's morally defensible, and I don't give a fico
for that guy Jesus." I'm not sure why we'd call the first person a "Christian" but not the second. It seems that the first is a "Christian" only by happenstance -- if he had learned of the "golden rule" from a fortune cookie rather than the bible we could, with equal justification, call him a "Fortune Cookiean." If "Christian" is to be a meaningful category, it must mean more than just thinking that Christ was a smart cookie.