While I didn't give a detailed response to the first post which was a single sentence, I've clarified what I would do in my home campaign which you are ignoring. I would base any response to burning down a village on several factors. I should also note that I don't care why the village was burned down and I assume that not ever single individual from the toothless grandmother to the newborn baby residing in the village is responsible for the lynching.
So the fact that it was relation for a RACIALLY MOTIVATED LYNCHING doesn't factor at all? That nobody in the community tried to stop them is a tacit approval of such behavior.
I won't say more due to the politics rule on this board.
Why not? Magic exists and it would be logical for someone important in the village to have a sending stone to contact someone else in case of emergency or vice versa. If it wasn't magic, when the PCs started burning the village did they kill everyone in the vicinity and there's no chance of someone escaping? If so, how? Unless the PCs have a small army of hirelings, I see no way they could have stopped everyone.
I didn't realize your setting was Eberron where magical telegraphs exist between po-dunk villages. Then again, I would hope a setting so magically advanced would have moved passed lynch mobs, but then again, I live in 21st century America so I guess its naive to expect that.
Unless the group somehow massacred everyone in the village, everyone working in the fields, everyone who could possibly know what happened, why would people would let others know what happened. Why wouldn't it be believed? Traders stop by the town and see the smoking ruins and ask what happens - survivors tell them what they saw would be one logical way for the word to spread. Communities are connected by ties of family, friendship, culture.
And every person was close enough to get a good look at the PCs and was clear headed enough to remember distinct details. Nobody misremembered, nobody didn't get a clear look and made up details to fill in gaps. Nobody lied to settle old-scores or take advantage of an opportunity ("It wasn't travelles, its Old Man Wicker whose hogs keep eating my turnips. I saw him learning fire magic from a devil!")
In the most recent mass school shooting, several people reported contradictory descriptions of the shooter, even leading to a false arrest. We have camera phones and high-speed wifi and we couldn't get our stories straight. Yet a bunch of farm hands in the field smelled smoke and rode into to town and can give perfect descriptions of the PCs?
I grew up in a small town and there was a bank robbery before I was born. Several people were able to give detailed descriptions of the robbers and their vehicle because everybody knew everybody and strangers stick out like a sore thumb.
And yet D.B. Cooper was never caught. Lots of people ride into town and ride out without ever being caught. Whole Podcasts worth. Even in an era of advanced forensics and DNA matching. Sometimes, the criminals move on. Most of the notorious outlaws in the West had long and profitable careers despite their notoriety.
I clarified my response on this because I wasn't clear in my initial one line response. Depends on the details of where the village is, what the local government it like, what the resources are. Word will likely spread and I'll judge the response based on that. Best case scenario for the PCs is that people are likely to recognize them as murderers or at least with suspicion - after all how many heavily armed small groups are running around the countryside? Depending on the area there may be wanted posters or the government may hire someone to track the group down and bring them to justice.
The original poster (who I realize is not you) said it was an area under the influence of a raksasha and thus a PC tabaxi would be mistaken for one and lynched. No further info was provided but village. My take was that it seemed particularly convienent that all of a sudden the entire nation gained knowledge of the PCs guilt.
In the video game Elder Scrolls Online, if you are caught committing a crime (pickpocketing, murdering, or assault) a bounty is placed on your head. As long as that bounty is active anywhere you go IN THE MULTIVERSE (ESO has planes like D&D) citizens will react hostile to you and guards will accost you. If your bounty is low, they will just demand you pay the bounty and surrender any stolen items, but if its high enough you will be attacked by every guard in the Oblivion and Nirn. That's what this scenario reminded me of. One NPC catches you and every guard across the multiverse is hunting for you. That's fine for a video game, but I always viewed D&D as having a slight amount for nuance.
There are a lot of factors here and variance but it wouldn't be unreasonable for things to escalate to the point where a small army is hunting down the PCs. They may be powerful but I'm not going to limit the response to what I think the PCs can handle, I'm going to make the response fit the crime and the region. It could be anything from getting a bad reputation to being forced to pay a weregild (GP paid in compensation for the crime), jail, being hunted down, nothing at all. It will always be something that I judge logical for the crime and the region.
YOU judge. That's the point. YOU, AlViking, have sat in judgement of the PCs and found them guilty. Of course Every NPC is going to believe they did it, you know they are guilty and you control every NPC! There is no situation where the PCs ride off and aren't punished for their crime. The world itself will bend to make sure of it.
What players can't do in my game is assume that their actions have no consequences or that the consequences of their actions will always be something they can handle.
So, hypothetically, can they not just leave? Go to a different country? Opt to get on a boat for a different continent? Become pirates? Or is the arm of the law always going to find them? Is the king of the nearby nation going to extradite them? What if they join the BBEG in exchange for protection? Would you allow it? Or is the universe always going to find a way to answer this crime?
Player decisions change the course of campaigns all the time but they still live in a world where they can't assume they an get away with whatever they want to do.
I find those two sentences exclusionary. I don't disagree that actions have consequences, but if the players decided that those racist villagers had it coming and now the game has taken on a form you didn't prepare for (they join the bad guys, become a bandit gang, or leave to a totally new part of the world) are you fine with this or does the campaign end because they did want they wanted to do?
Same old accusation that has is not true now and has never been true.
Jury remains out.