Very good. Put simply it is applied to those outside of. The villagers were outside cities and therefore difficult to preach to,
Cite?
and also often would incorporate outside teachings with what they were taught.
That excludes Paul from all of ancient "Christendom" then since Hebrew and/or Christian doctrines were outside teachings in his homeland of Tarsus.
There is nothing inherently evil about anything pagan.
That's good, since the cults you will call pagan are re-invented in the myths, legends and fables of Christianity, as opposed to the usage among non-Christian cults, most notably non-Christian Roman cults.
Jewish names were often changed to pagan names when Jews were, for example, among the Babylonians or Greeks.
You mean like when they were living in the Sumerian city-state of Ur, as they claim, before they left for the arid hellhole that was supposed to be a Promised Land? Of course that commits another anachronism, since it now requires us to force the camel of Pre-Roman Babylon through the needle of a Roman era idiom.
The Jewish calendar is full of "pagan" influence, as is our own.
The purpose of my post was to remind you that labeling your enemies as pagans commits an anachronism. What you intended to say is that these other cultures are/were your enemies. Or you may prefer to call them superstitious. But whatever you call them, if it disparages them, it disparages your modern version of the myth, legend and fable they invented, which was the basis for the myth, legend and fable your parent cults handed down to you, most notably those dastardly Catholics, who invented this nonsense to begin with (before the schism; noting that you haven't accounted for the history of the Ethipian, Coptic, Sryiac, Greek and Russian sects of the main line of early Christian orthodoxy).
As for the calendar . . . that's a distinct issue, involving the recognition in more than one culture (and across many religious cults) that there were difficulties in standardizing to any system of time that did not account for the non-integer number of days it takes the Earth to complete one orbit, together with the irregularity of mixing lunar and solar cycles. Of course some modern religions still are stuck in the era when scientists could be exterminated for merely reporting facts which controverted their superstitious beliefs . . . which makes the idea that there is a pagan influence in the calendar a little more than ironic. There is some evidence to suggest that the mystical interpretations of the Sun and Moon probably was brought out of Persian and into Egypt, the Levant and esp Syria/Anatolia by the movements of Greek and Persian armies across that natural bridge.
The baptism is also pagan in origin.
There is no historical evidence about the origin of this or any other early Christian ritual. It's a Greek word, as is all of the Christian text. Greek culture and tradition had already fused itself into cultures of Northeastern Africa, the Levant and Anatolia long before the sect that became Christianity established itself. Jesus of the Bible (as opposed to the Agnostic versions of him) more closely resembles Socrates and the principles of Stoicism than anything remotely related to Hebrew culture. There is some speculation that ritual washing established itself among the Essenes, whose quarrying activities led to the construction of a number of underground bath houses. But it makes no sense that they preserved this in connection with the Plato's icon of Greek virtue, just as no one has any idea if this legend was created in the Levant, or in Alexandria or Tarsus, where children of the Hebrew refugees of the Roman War of ca 70 AD had fled to safety, and/or been taken there as captives of legionnaires, esp. as captive brides of Roman soldiers, which appears to be the legacy which influenced Paul of Tarsus. That's assuming Paul is a real person, which is impossible to say. All we know for sure is that some of the extant text which purports to be Pauline is forgery. And it remains unclear how the synoptic Gospels, the Gospel of John, the Pauline Epistles and the remaining texts preserved for all of Protestantism by those dastardly Catholics, relate to one another canonically, geographically or otherwise. It's all just a blur of wild imagination.
[baptism originated from] A public proclamation adopted by early Christians.
Here you appear to be conflating early Christianity with not-so early Christianity. In any case there is no evidence other than than the influence of Hellenism, syncretism with distant cults, and the likelihood of bathing rituals among the Essenes.
Hell, the trinity, the immortal soul, the cross and holidays and the rapture are pagan,
That is the way it might have been cast among various Christian heretics of the Medieval through Victorian periods which creates another bizarre conflation of historical nonsense with another anachronism. But you will not find any scholarly work of recent publication that labels non-Christian sources as pagan. Again, by the implied definition of the term as you are using it, all of Christianity, and all of Judaism are pagan in origin. All religion is superstition, myth, legend and fable invented to explain phenomena for which there was no science. "Pagan" is no more valid a term of disparagement than "Gentile".
but differ from baptism in two important ways. Firstly the latter are specific religious teachings or practices of a pagan nature and secondly they are unsupported by, and in conflict with the Bible.
You mean with your personal interpretation of the Bible. The majority of Christians believe differently than you do. And the majority of the world discounts the Bible altogether.