On only a few occasions have I had pressure from a passenger; more pressure in the past has come from employers than passengers.
During medevac operations, I held to a firm policy of taking no interest in the patient's condition or needs; that was the domain of the medical personnel. I confined my decisions strictly to safety of flight. I was open to requests from the medical crew, but mine was the final word, not theirs, and mine was based only on safety of flight issues. If we could do it safely, we did it. If we couldn't, we didn't.
On several occasions I made decisions which may have had significant ramifications for the patient. Once I turned back during a heart recovery when destination weather decreased. I informed the harvest crew of doctors, and returned to our home base. My understanding was that the recipient of the heart was being prepped, as was the donor, but conditions were not safe for the destination for arrival or departure with no deice and freezing fog rolling in. It would have done no one any good, and wasted the heart, I'm sure, to significantly delay departure, and would have only made things far worse should we have had an incident.
I wasn't on the next shift so I don't know if the harvest was made or not. I may have to face the possibility of having just denied a recipient of his new heart: that was not my concern, and it was strictly a safety of flight issue.
A passenger came to the cockpit one too many times on a fractional flight, screaming and yelling about running out of his favorite mini-bottles of scotch (his wife was stealing them), and not having his favorite tissue. He told me I was a liar and a cheat (he was upset about a fuel surcharge), and got in the way. I finally ordered him to his seat and ordered him to shut up. I told him I'd had enough. I informed the company by satphone, and continued to the destination where I dropped him off uneventfully.
On another occasion with the same fractional operator, during a company-arranged fuel stop, the passenger became irate, screamed and yelled and stomped his feet like a child, and called me several names I'd never heard before. I politely informed him that I was grounding the airplane and that I wouldn't permit him back on board in his condition (he had been drinking on the previous leg). He made demands and informed me that he was a personal friend of the CEO, threatened my job, threatened me, and ordered me back into the air. I refused. Problem solved.
I don't make flight decisions based on pressure; I make them on safety of flight, and given a choice between finding other employment and bowing to pressure, I can always do something else. The same goes for pressure by employers. I've never had a job I've not been willing to shuck in a heartbeat on principle, where safety of flight is concerned. It's a matter of integrity, and I ensure the employer understands that. A good employer respects that position, and a bad employer isn't worth working for.