Never lose your cool. Smile and talk to them like they are a three year old.

Stick to policy and let the manager be the one who breaks the rules.

If you do it, then you can be punished.

Some people cause a scene to bully you into breaking the rules and get free stuff. In most cases I just become super nice (like syrupy, sickly sweet) and pretend I'm on their side (bag fees are dumb), and let them know you don't want to lose your job for giving away free merchandise (so sorry, did you still want to buy a bag?). If they are super toxic, you call a manager and make them deal with it, that's what they get paid for.

Your colleague is a dick for not backing you up.

When I was in retail (Apple Store), we had a saying “Don’t feed the bears”. Meaning if you give in to petulant outbursts, the offender will keep coming back and asking for more.

One CO worker looked a rude old lady right in the eye and said "ma'am this is a place of business. When people do business they have to operate with mutual respect and trust. If we don't trust each other to do our end of a transaction, we can't exchange anything between us. If we don't respect each other, we can't exchange anything between us. I've been acting in trust and respect towards you, are you going to do the same for me? Because if you can't, we can't do business."

She immediately stopped being bitchy and was never a problem again. It was the wildest shit I've ever seen.

I'm working in customer service and we sometimes have people who don't want to pay for a service we offer (fixing their stuff in IT). There are two options:
You tell me what you did when and ask nicely if we can fix it for free? You just did half of my work, of course I will make an exception for you.

You blame everything on us and want the service for free as a compensation? Bet I will invest more time to prove why it's your fault and therefore you'll have to pay for it.

For a plastic bag? Give it to them, it costs nothing and it's not worth your time and effort.

I've been in customer service in various roles for over twenty years. I've spent the last six in different positions in animal shelters, veterinary clinics, and am currently at a pet food manufacturer. Anything involving people's pets leads to highly emotional situations, especially when things don't go the way pet owners are hoping. I've dealt with people on some of the worst days of their lives. This leads to a lot of heated interactions.

You're absolutely right, your coworker's choice to give in to this man's tantrum is not how that should have been handled. It rewards Karen's nasty behavior, and it sends the wrong message to other customers. Staying calm, explaining policies simply, and not becoming defensive or arguing points that don't matter is important. My golden rule is to avoid letting a customer get a reaction out of me by all means necessary. I usually tire them out with calm kindness and repetition, because they're used to making people uncomfortable to get their way. I've got all day, Karen. At least I'm getting paid for this, while they're wasting their own time.