This might work very well for you - but I find that rude remarks like that often end best if I simply respond to the professional part of the remarks - namely what the client wants to achieve, and how they handle it in their frustration.
But - and I think this is important - we all have a personal place where we draw the line. What I might be able to overlook, you might see as extremely offensive. And like I said in the original post, it’s totally fine to assert that you’re not accepting any rudeness. We should never have to accept bullying or rude comments - but how we handle them is the key to success in this situation.
So I agree with you that you should let them know it’s not ok to be abusive. But I would maybe start by apologizing first, and then move on to my remark about their rudeness. That affirms your position as polite and calm, yet sets the boundaries for the communication…
I try to think of myself as a customer support representative. If I was working for a big corporation, I would never ask the customer to apologize to me for their rudeness. I would maintain my calmness, and work to try and solve the issue. If I started requiring the customer to apologize before I was willing to help them, that might cause you to get fired, or at least having a reprimande at work, and would probably cause the client to become even more pissed off.
In these cases, I’m representing myself, as my own brand, and I want to behave in the same manner towards my clients as I would if I was working for someone else.
Thanks for your input!