Reading this question, the accepted advice for killing a player is to talk to them first.
My campaign is run in a Game of Thrones style setting; the good and honorable die doing what is right, and actions have consequences.
I have made this very clear at the beginning of both sessions we have played and they all say they understand, though their actions give a different impression.
I have a gnome monk that wants to spread the truth that the world is round. He tells everyone: NPCs, bandits attacking him, terrified hostages they have rescued. Sooner or later the establishment is going to get word of this and put an end to it; the Dark Ages were not known for their tolerance of heretics.
The two clerics think they're the front-line fighters and have a "shoot first, ask questions later" attitude.
There will be no resurrection or dice fudging; I have made that clear, too.
It is almost inevitable that one of the PCs will die next session. I have spoken to them in and out of game and they still act like their actions have no consequences. They say things like, "If we couldn't kill it, why would you place it here?"
When the time comes and one of them gets himself killed, how can I do it in a way that wont have him moaning as he fills out a new character sheet?
Best Answer
It all comes down to agency. What choices are the players making?
If you are spoon-feeding them encounters, which they have no options but to engage, then yes, it's on you to make sure those encounters are survivable. If they are choosing what to do and what to engage, then the responsibility lies on their heads, not yours.
Let's look at two possible situations.
Situation 1
The PCs are in camp when some raiders attack. Oh noes! They wake up, but the raiders are surrounding them. They have no choice but to fight the raiders, and they are of such number and ability that at least one PC death is, essentially, inescapable.
Situation 2
The PCs are in a town when it is about to be attacked in force. They can stay and help the town defense, in which case it may stand. They may also flee the town, in which case the attackers will almost certainly win.
However, the attackers are of such force and number that if the PCs decide to stay and defend the city, it is highly likely that at least one of them will die.
Choice is the difference
In both of these scenarios, the PCs are faced with a fight that they might not survive. However, in the second one, they choose to get involved in that fight. It is their choice to risk their PCs to keep the town standing (or not). Not only does this put the responsibility on their head, but it also gives them a chance to be truly heroic. These types of choices (what am I willing to risk?) are some of the best moments in roleplaying, especially when real risk is on the table.
It's okay for PCs to die! But they should do so as a result of choices they make, not encounters that the GM "throws" at them.
Try a Clock
For the specific case in the OP, consider something like an Apocalypse World front's "clock". As the PCs engage in activities that will cause unwanted attention, you can increase the "clock" and the tension/heat that the players will encounter. This gives them an idea of the seriousness without making it an immediate "you die" moment. It also gives them the choice to continue with what they're doing or not.
So, for the "heresy" clock, the stages might look like this:
Stage 1: Mutterings of heresy. Some of the townsfolk talk about a new heresy they've been hearing.
Stage 2: Known heresy. People talk about this crazy new heresy they've heard about, with specifics.
Stage 3: Official pronouncements. There are proclamations that the heresy is in fact against the church.
Stage 4: Public trials/executions. Heretics are found and imprisoned or killed.
Stage 5: Manhunt. Wanted posters are put up for the lead heretics (aka the PCs). Movement becomes difficult.
Stage 6: Assassin squads. Exactly what it says on the tin.
You can then advance the current stage based on time or PC actions. This will give the impression of advancement and real change in the setting, give enough of a social movement to warrant the church's actions, and, perhaps most importantly, give the PCs plenty of warning that continuing on this path will result in dramatic consequences.
And that may be cool! This kind of "heresy plotline" may be exactly what the players want, and so letting them play through that may totally make them happy.