I'm currently having trouble with this.  I live in America, and naturally, every workplace I have a job at is chock-full of people who are not only nonbelievers, but actively revel in promiscuity, drugs (mostly weed), petty theft, ect.  I know I'm supposed to behave cordially with them, but I feel like if I get too "chummy" with them it will not only further legitimize their life-styles in their eyes, but will also be an affront to justice to treat an unrepentant sinner as you would treat a penitent.  How are you to act, typically, in everyday interactions with these people?

I'm currently having trouble with this.  I live in America, and naturally, every workplace I have a job at is chock-full of people who are not only nonbelievers, but actively revel in promiscuity, drugs (mostly weed), petty theft, ect.  I know I'm supposed to behave cordially with them, but I feel like if I get too "chummy" with them it will not only further legitimize their life-styles in their eyes, but will also be an affront to justice to treat an unrepentant sinner as you would treat a penitent.  How are you to act, typically, in everyday interactions with these people?

Welcome! You sound quite young, and have probably not acquired the ability of walking the fine line between "behaving cordially" and "getting too "chummy" with them".

The first step is to daily pray for these people. Then treat them with reserved politeness, remembering that many of them have never been given the same chance to learn virtue as you most probably have. Don't be concerned about making friends in such an environment and remember why you are in that environment: to earn a living by doing your work to the best of your ability.

It is not your place to judge their behaviour, just pray and be a good example. Being polite is not to legitimise their behaviour. Your different behaviour will be noticed by them and may make them feel uncomfortable and may cause the to keep their distance or even resent or ridicule you, but don't be deterred by that. It may bear good fruit

Just do your job and stay away from conversations that can lead to more.  Bad company, they are.  Prays are strong for them. My husband got into conversing with people in the hospital.  Of all places you would think they would all be busy!  It brought him to mortal sin.  So, stay away from conversation, stick to job and go home.

With my generation, it's hard to "get out", because they all act like this to some degree.  I have yet to meet a single person my age that doesn't openly revel in porn, or going to strip clubs, or "smoking that weed, dude!", ect.  Even many of the older guys do it too.

It's nothing new, been the same since the 1960's. The sɛҳuąƖ promiscuity was worse than today in the  late sixties and 70's, nobody young needed to go to a strip clubs.

Nadir's advice is perfect. The only thing I will add, is that when they talk about drugs and porno, you can make a joke of it, like dismissing it as idiotic. They will not understand the religious aspects, so speak to them from uncommon wisdom of the world, while making a laughing matter out of the whole affair: 

Weed - "I do not have the time to confuse my mind and get knocked out by weed, I don't even waste my time watching television or playing video games or texting all day. I have studying to do and things to learn to make a good living. This is the time to get ahead, while I am young, all the older weed heads I see are all poor bums."

Porn - "I do not understand why a young healthy man would want to watch porn, what's it good for? It just gets you frustrated. I'll use my time to improve myself and learn about what life is all about and how women behave, so I can have a good wife for life, rather than an illusion in strip clubs and video."

sɛҳuąƖ promiscuity - "Any girl that is easy, is easy with everybody, so don't think that you are something special. Promiscuity means herpes for life or worse. No, I seek the girls that no one can approach."

Just do your job and stay away from conversations that can lead to more.  Bad company, they are.  Prays are strong for them. My husband got into conversing with people in the hospital.  Of all places you would think they would all be busy!  It brought him to mortal sin.  So, stay away from conversation, stick to job and go home.

What is your age?

From the Fathers of the Desert;

The same lawgiver who said, "Thou shalt not fornicate." also said, "Thou shalt not judge."

From the Fathers of the Desert;

The same lawgiver who said, "Thou shalt not fornicate." also said, "Thou shalt not judge."

The "not judge" commandment is terribly misunderstood and abused nowadays.

Most people rather take sides with the one in the left here, instead of Jesus Christ:

You're young, it would be worthwhile to get whatever training you need to work for yourself - or in a more upscale environment where those types at least keep it to themselves for the most part.

I'm working on it.  That's not going to start for at least a couple of months though.