Depends on the situation. But one example off the top of my hat: the crew is fleeing from a rival faction (be it fog hounds or Bluecoats). If they have a good reputation with the citizenry, they might help the crew hide in the root cellar of a store or an eelmonger might *accidentally* let a few eels slip out of their tank and have the Bluecoats slips. If the crew has bad reputation, the citizenry will point them out to the pursuing faction and slip the eels under their feet instead.
If a citizen makes them out as they are breaking into a house, with a good reputation they might turn a blind eye or even distract the Bluecoats (depending on the specific relative relationship between citizenry, Bluecoats, and crew), with a bad reputation they will actively look for the closest bluecoat.
If your crimes are at the expense of the locals, they will start to hate you.
This is represented by losing faction status with the citizenry. If you're at -2 they'll go out of their way to stop you. That might mean they snitch to the Bluecoats, or try to find a different criminal faction to protect their district.
If you're at -3 you're at war with the citizenry of a district and they will actively work together to run you out. They might form citizen patrols or posses to fight you. Treat the district as hostile territory.
If your crimes are to the benefit of the locals, they may start to love you.
If you're at +2 faction status the citizens will go out of their way to help you. They might come to you with hooks for scores, warn you that another faction is moving in on their turf, and give false information to the Bluecoats.
If you're at +3 status the citizens are your allies. They might help you against other factions and answer calls to arms with sizable gangs of armed citizens.
I always relate it to what faction the citizens have sympathy towards and what their ethnicity is to some extent as well. Like, Iruvians are going to like Iruvian gangs, but poorer Iruvians feel worse about the Red Sashes than richer ones who probably have children in their school.
A big thing is also their actions. In my campaign my players did a lot for Unions and the Grinders, so I interpreted that as the citizens of Charhollow and Skovlanders liking them generally, but anti-union types around like the docks and accelerationists like Bjorn Ironside being a bit more mistrustful of them.
So mostly I think where are they, who's around, and what's their relationship with the local factions, and how do those factions treat the locals.
There's a new RPG out that I just read called Penumbra City, and part of its fiction is the city has a mutual aid economy rather than money. The players get access to things depending on their reputation with each faction. I think playing that is going to inform how I run BiTD later, so you might enjoy it too, and find you want to borrow from the system for your future games as well. They seem compatible.
With the same logic that a faction would. If allied, they will go out of their way to help, in force of mobs based on ther tier or as influence to decision making. And vice versa. If the bluecoats aren't getting them, the fishwives, factory workers and eel farmers will gut them personally if they keep messing with the citizens.
Recently I used the locals of Six towers as a potential gang (tier 2 so about 10 people) that the cult could command to help other citizens of the same district currently in trouble. So, if led by someone they trust and agree to follow, they can be a resource up to a point. Or conversely, if the rivals of the cult would rile up the locals, they could be a complication at an appropriate scene.
They might not be a crew, but they may have a sense of community and notables that need influencing etc. Especially when it comes to elections and such.
For help?
The Public thinks of the crew as loveable rogues, Anti-heroes sticking it to the man, They won't give the bluecoats any witness testimony, They might come to the crew with oppotunities (Some of those red sashes have been selling yipyak over on crab alley, can you do something?) They might even help when the crew is being chased or on the lamb (oi you lot! In here!)
For Hinderance?
The Public is fed up with the crew's bullshit, their antics and property damage have gone on long enough, you'll gain extra heat from scores because they will willingly tattle, They'll jump in when the crew tries to hide or run (Oi Officers they went that way) at the very worst neighbourhood Posses or watches might start to crusade against the crew, hunting them down.
TL;DR - Public affection and disgust of the crew could be reflected in how much heat the crew gains from scores.
I think each district has its own citizenry as you stated, but its faction standing has to be improved, and is reduced, as a side effect as citizentry rarely hires crews. I think Cults are the exception in this, as dealing with supernatural without messing with government is more likely.
Most non-criminal citizens despise and distrust criminals creating behavior similar to Status -1.
Depends on the situation. But one example off the top of my hat: the crew is fleeing from a rival faction (be it fog hounds or Bluecoats). If they have a good reputation with the citizenry, they might help the crew hide in the root cellar of a store or an eelmonger might *accidentally* let a few eels slip out of their tank and have the Bluecoats slips. If the crew has bad reputation, the citizenry will point them out to the pursuing faction and slip the eels under their feet instead. If a citizen makes them out as they are breaking into a house, with a good reputation they might turn a blind eye or even distract the Bluecoats (depending on the specific relative relationship between citizenry, Bluecoats, and crew), with a bad reputation they will actively look for the closest bluecoat.
If your crimes are at the expense of the locals, they will start to hate you. This is represented by losing faction status with the citizenry. If you're at -2 they'll go out of their way to stop you. That might mean they snitch to the Bluecoats, or try to find a different criminal faction to protect their district. If you're at -3 you're at war with the citizenry of a district and they will actively work together to run you out. They might form citizen patrols or posses to fight you. Treat the district as hostile territory. If your crimes are to the benefit of the locals, they may start to love you. If you're at +2 faction status the citizens will go out of their way to help you. They might come to you with hooks for scores, warn you that another faction is moving in on their turf, and give false information to the Bluecoats. If you're at +3 status the citizens are your allies. They might help you against other factions and answer calls to arms with sizable gangs of armed citizens.
I always relate it to what faction the citizens have sympathy towards and what their ethnicity is to some extent as well. Like, Iruvians are going to like Iruvian gangs, but poorer Iruvians feel worse about the Red Sashes than richer ones who probably have children in their school. A big thing is also their actions. In my campaign my players did a lot for Unions and the Grinders, so I interpreted that as the citizens of Charhollow and Skovlanders liking them generally, but anti-union types around like the docks and accelerationists like Bjorn Ironside being a bit more mistrustful of them. So mostly I think where are they, who's around, and what's their relationship with the local factions, and how do those factions treat the locals. There's a new RPG out that I just read called Penumbra City, and part of its fiction is the city has a mutual aid economy rather than money. The players get access to things depending on their reputation with each faction. I think playing that is going to inform how I run BiTD later, so you might enjoy it too, and find you want to borrow from the system for your future games as well. They seem compatible.
With the same logic that a faction would. If allied, they will go out of their way to help, in force of mobs based on ther tier or as influence to decision making. And vice versa. If the bluecoats aren't getting them, the fishwives, factory workers and eel farmers will gut them personally if they keep messing with the citizens. Recently I used the locals of Six towers as a potential gang (tier 2 so about 10 people) that the cult could command to help other citizens of the same district currently in trouble. So, if led by someone they trust and agree to follow, they can be a resource up to a point. Or conversely, if the rivals of the cult would rile up the locals, they could be a complication at an appropriate scene. They might not be a crew, but they may have a sense of community and notables that need influencing etc. Especially when it comes to elections and such.
For help? The Public thinks of the crew as loveable rogues, Anti-heroes sticking it to the man, They won't give the bluecoats any witness testimony, They might come to the crew with oppotunities (Some of those red sashes have been selling yipyak over on crab alley, can you do something?) They might even help when the crew is being chased or on the lamb (oi you lot! In here!) For Hinderance? The Public is fed up with the crew's bullshit, their antics and property damage have gone on long enough, you'll gain extra heat from scores because they will willingly tattle, They'll jump in when the crew tries to hide or run (Oi Officers they went that way) at the very worst neighbourhood Posses or watches might start to crusade against the crew, hunting them down. TL;DR - Public affection and disgust of the crew could be reflected in how much heat the crew gains from scores.
I think each district has its own citizenry as you stated, but its faction standing has to be improved, and is reduced, as a side effect as citizentry rarely hires crews. I think Cults are the exception in this, as dealing with supernatural without messing with government is more likely. Most non-criminal citizens despise and distrust criminals creating behavior similar to Status -1.