This is something that I cover in my CRM courses, having been slung off a job once or twice for refusing to perform certain functions, and even having to threaten to counteract violence. I worked for a company once that responded to a request to change a female pilot because her boobs didn't bounce as much as the other one employed by the company. The fact that she had also refused to take a heavy helicopter out of a very small hole appeared to have nothing to do with it. This was in Canada, a place where passengers on the oil patch routinely refuse to wear shoulder straps in the front seat, so it's not only in the Gulf that this stuff happens. This one resulted in a stand-up argument in the ops room with senior management who were simply too stupid to realise they were digging themselves into a deeper hole. And don't get me started on refuelling helicopters with the engine running and nobody at the controls (yes, I know there are circumstances in really remote place where it just might be acceptable, but not when there is a medic sitting in his van all day reading novels).
Before I started flying I was very lucky (if you can call it that) to be in Transport & Movements (in the Army) and telling Generals (as a corporal) that they couldn't get on planes back to UK. Believe me, in the military, you soon learn to be diplomatic in such circumstances! If I got a really stroppy one all I had to do was invite him to pick up the phone and speak to the other General on the end of it.
As one who has been there, I can assure younger pilots of one thing, that, a walk on the wild side though it is, you simply have to say NO sometimes and risk your job. You might lose it, yes, but the results come back in spades some time later, because this industry is very small and the people that are worth knowing and working for hear about it and you will get work in the right place. This is not to say you should be rude to customers, but you must be firm and stick to your guns. The ultimate, of course, was Hugh Dowding who told Churchill he wasn't going to have any more Spitfires sent to France, but the principle is the same.
"I'm sorry sir, I can't put you on that frozen lake because I don't know the state of the ice, especially as you've just drilled a big hole through it, but I can land you on the shore and you can walk 50 meters across to it."
There's the key - always offer an alternative if possible. Look them in the eye, do it politely but firmly, and you will eventually be respected.
One way of looking at it is to realise that people who are putting the pressure on want something that you have, so you really have the upper hand, if you think about it.
Good luck!
Phil
"I have never taken disagreement as an indication that I am wrong."
Enoch Powell