I'd argue that the political bias is the other way around; King James had every reason to want to justify the anti-Semitic violence characteristic of his family line and the contemporaneous law of the land. Whereas the NIV board has less money and violence invested in anti-Semitic language, though the translation is not entirely free of criticism on that front.
If we look at the original text, I'd argue that either translation is valid, but that the KJV translation probably comes closer to the sense that the verse's authors intended. The Textus Receptus, the Greek edition that James' translators were using, records this verse as:
εσται δε πασα ψυχη ητις αν μη ακουση του προφητου εκεινου εξολοθρευθησεται εκ του λαου
The key term is bolded: εξολοθρευθησεται. Interpreting it is a slight problem, as it is only found in this text; no exact equivalent is seen in any other Greek text. The usual method of interpreting by examining context of existing cases is therefore impossible, and it makes it very hard to get the sense, or connatation, of the word as it would have been perceived by its original listeners. This leaves only morphological analysis, which is usually better at explaining etymology than implication. But it does cast some light on the probable meaning of the term. This is a fairly complex verb, a phenomenon much more common in Greek than in English. Its root word is problematic, as it does not exist at all in the historical record and can only be inferred from the structure of this instance of it: ἐξολεθρεύω. No certain definition is possible here. But this root, whatever its meaning, is almost certainly itself derived from ὄλεθρος. This is a much more common word, and it means, straightforwardly, "destruction". We see ὄλεθρος used to describe scenes of utter devastation throughout the New Testament, from the description of the Apocalypse in the letters of Paul to Thessalonia to the descriptions of Satan's destruction of the soul in Hell in the letters of Timothy and that to the Corinthians. Always heavy stuff, and notably, always the work of supernatural agents, in both Christian and non-Christian texts. Destruction beyond what mundane human violence could possibly accomplish. Divine retribution seems strongly implied here.
The rest of the mystery word are affixes, though, and subject to interpretation. "-εύω" makes it a verb rather than a noun. "ἐξο-" usually means "out of" or "from" and is one of the more common prefixes in Greek morphology, carrying a wide range of potential meanings. The other modifications are conjugations, making this a Future Passive Indicative 3rd Person Singular, ie something that "will (factually, not speculatively) happen to him".
A further wrinkle is that for the original authors, this whole sermon was actually a reference to an older text, the popular Greek translation of the Hebrew Scriptures known as the Septuagint, or LXX. The verse Peter is quoting here is found in the book of Deuteronomy, Chapter 18, verses 15-19. In English, this passage reads “The Lord your God will raise up for you a prophet like me from among you, from your brothers — it is to him you shall listen — just as you desired of the Lord your God at Horeb on the day of the assembly, when you said, ‘Let me not hear again the voice of the Lord my God or see this great fire any more, lest I die.’ And the Lord said to me, ‘They are right in what they have spoken. I will raise up for them a prophet like you from among their brothers. And I will put my words in his mouth, and he shall speak to them all that I command him. And whoever will not listen to my words that he shall speak in my name, I myself will require it of him." A key passage for those Jews who believed in the coming of a future Messiah. Notably, it says nothing at all about detroying those who aren't on board, just that YHWH will "personally require" that they listen to his prophet. Threatening, to be sure, but pointedly vague. Both ancient and modern skeptics have argued that this position of "prophet" or "judge" in Moses' absence was originally meant to be a permanent office that many would occupy over time, as opposed to a single Messiah figure, and these powers were historically claimed by the Judean monarchy. But there you have it.
All in all, given the use of somewhat similar phrases in the NT, I think it is most probable that some kind of End Times, apocalyptic destruction is being implied here. Though not holy war, as you seem to be implying, as the original sspeaker would have been in no position whatsoever to wage one, this being written more than two centuries before Christians ever held real political power.
