Thanks for your points.
A pilot of a passenger airline interviewing all his passengers and checking their luggage to find out if anyone has either moral and religious believes
This has nothing to do with my question. I never talked about interfering with people individual rights or belief, I was talking about objecting to transport live animals destined to a cruel death as this may be against the pilot moral or religious belief.
Whether "the pilot is contracted to carry out the orders of his employers" is completely subjective. What would you do if your airline assigns you a flight to transport human beings destined to be sold as slaves?
While this example may sound exaggerated it shows that what is acceptable and what it is not is completely subjective, indeed a few decades ago it was perfectly acceptable for ships captains to transport slaves, nowadays thanks god nobody would accept to do that.
While it can be perfectly acceptable to you to transport animals which are destined to a whole life of painful tortures, some people can find it very difficult to accept that they are involved in some ways in the process of condemning an animal to endless brutal tortures and death.
In many countries people can object to military service due to their moral belief, I suppose there might be a legal way to object to do some duties your employer may request you to do. I obviously understand that if most of the duties involved in my job are against my belief I cannot expect to be relieved from all of them, and I should just not accept the job or quit. But if there are just a limited number of duties involving going against my beliefs why shouldn't I be legally allowed to request not to be assigned to those duties?