You might need to break this down a bit into separate questions. Otherwise, 'it depends'
In most cases it wont be a choice between refusing to serve or refusing to apologise, it will be a matter of whether you remained professional and to a point, respectful. Remember it's not entirely a matter of you being right or wrong, you are representing and speaking for the business also, so it's not always appropriate to apologise on it's behalf without thinking.
It also depends what 'lashing out' really means here. If someone is just getting a bit frustrated '***k's sake', talking over you and all that, I'll generally let that slide, it's often just a bit of steam and many will quickly say sorry 'I know it not you...'. If we're talking direct abuse, like calling me heavy nasty names, getting repeatedly in my face or worse, then yeah I'll refuse service or apology no problem, not putting up with that at work and any employer that said I should likely isn't for me.
I'm in retail (delivery driver) and I'd say that up until quite a high point my employer will have my back if I tell someone 'No', the customer can call, complain and call me all the things under the sun, the manager is going to make nice noises, ask me what happened and then we'll likely prob both laugh. As above, my employers main concern would be if I had remained professional in saying no and reporting back. I've had once instance where I had to use violence on a customer and they totally had my back, but again, stayed professional.