I think noticing that there is little to no evidence for the concept of "Free Will" as most people seem to understand the term has been the strongest influence on my emotions around things like murder and sex abuse and any other victim crimes (rather than victimless crimes like buying and selling sex).
Without a working concept of "Free Will" the need for retribution or revenge or the need to see the criminal suffer falls away entirely and is indeed replaced with things like sympathy.
This position - contrary to the response I have seen from some quarters over the years - is in no way in conflict with seeking justice again or incarceration of criminals. In fact often those things are untouched. But the focus changes from retribution and revenge and punishment to the protection of the pubic and rehabilitation. It is more a realignment of incentives than outcomes in other words.
As a random example some people might want to see a person who sexually abused a child to be locked away for a very long time. But if scientific and study data showed that a shorter time significantly reduced crime and recidivism rates then I would support shorter sentences (if!). Because my goal would be the reduction of crime and victims - not the punishment of the criminal and making the criminal suffer.
Similarly on the subject of child abusers I think it was on boards I recall some users speaking of one who they hoped would not only be locked up forever but would be routinely bullied and raped in prison. Again the focus here on revenge and seeing a criminal suffer is not one I can get into the head space of myself in the abscence of a workable "Free Will" concept. For me the answer to awful suffering is not sitting around hoping for even more suffering.
But yes I feel "sympathy" for all criminals even the worst ones. I feel sympathy for Hitler even. We do not choose our genes. Our parents. Our upbringing. Our circumstances. Our brains and compulsions. Or pretty much anything else. And it seems without much evidence for Free Will we do not really "choose" anything. As such deep empathy and sympathy for even the worst criminals among us is in no way mutually exclusive with Criminal Justice and Law.
I do not have much time for Religion or Christianity as my posting history shows. But one thing the Jesus Character and his followers did not get wrong is certainly the concept of "Hate the sin not the sinner".
Not a directly reply to your post but rather using your post as a spring board to elaborate on what I already said above: With killing people one should indeed think they need to find an "excuse" or a "justification". And I doubt in many cases they will be able to provide one.
I see no such requirement with becoming any kind of sex worker given there is nothing immoral about it or wrong with it in and of itself as a decision. Except if it is actively illegal to do so of course - then one should of course be expected to justify their decision to break the law (for example - it is a whole conversation often worth having when breaking the law as a form of social or legal protest is justified or not).
Where something is not illegal however - then we should expect to hear why someone is required to "justify their behaviour" or choices in each context on it's own merits. Innocent until proven guilty. A society should first show there is something to "justify" in the first place - before we go around pretending anyone has to justify anything. Similarly we should establish that there is something to actually feel sympathy for - before thinking we are required to feel any.
There is nothing wrong with sex work that I can see or have been shown on this forum - nor is there seemingly anything wrong with paying for sexual services. So there is nothing for them to "justify" or "excuse" in the first place in that context. Often the contrary is just moral high horsing ones own perfectly ok life decisions over someone else's perfectly ok life decisions. .
To answer the OP directly on the subject of prostitution therefore - I would reserve my sympathy for anyone who finds themselves in a career they themselves do not actually want to be in and wish to get out of. Whether they be a sex worker or a neurosurgeon or a politician or a sales clerk or anything else. Someone could have the "best job in the world" on paper and I would feel sympathy for them if they actively hate it and want out.
I have zero sympathy for people solely because of what career they happen to be in in other words. Otherwise that would be my value judgement in play - not theirs. And I am not in the business of feeling sympathy for anyone who does not require it as I would then merely be projecting how I imaging I would feel in their circumstance - rather than trying to find out how they themselves feel about it.