Just wanted to add here, that just because a girl has worked out how to screen out creeps doesn't mean she is some kind of hardened person who doesn't wear her heart on her sleeve. The two aren't really related. Being a sensitive, gentle person has little or nothing to do with being good at screening or poor at screening. Good screening is a skills based on learning and adapting.
I am retired now but I was really sad to leave the job as I enjoyed it very much. I never felt like I had to 'deal' with a lot of nonsense from these type of guys who arent even actually clients. That wasn't because I didn't get them trying to contact me. It just becomes part of your routine to screen them out and the more you do that, the less it impacts on your day because they don't get far enough into their messed up fantasies with you. We know for a fact that they are contacting 100 girls a week from their bedroom so the first thing I make myself think if if something starts to upset me, is that it is not personal to me. The first few months as a newbie were an eye opener for me because before you do this job you don't really realise how many weirdos there are out there. However you start to learn that that there are an awful lot but that most of them are just cretins sat behind a computer. Obviously when you get the email or call every single girl thinks 'uughh gross!'. No one is absolutely ok with this. But it takes a practice and 'mind training' to minimise the impact on your own mental wellbeing.
However just because a girl hits delete or puts the phone down and then goes to make a cup of tea rather than getting into communication doesn't mean that she is a person who doesn't wear her heart on her sleeve. With real people, whether it's family, friends, clients or even people who I have only just met I very much do. I am known among people that I know for crying over absolutely anything remotely emotional on TV and I am known for being a very caring person. I was a very efficient screener but by no means some kind of robot escort, hardened by the industry. If anything the industry made me more empathetic and improved my social skills, but it did sharpen my instincts and made me better at asserting my boundaries, emotionally or otherwise.
The distress you have been feeling is completely understandable and I really feel for you as we have all been there, and it is completely deplorable that these creeps try to seek out vulnerable women in this way to deliberately frighten and distress in the first place. However, the logic you seem to be following is that if you move to a mental space of coping with this type of communication, you will have changed your personality, and you will be somehow be a different and harder person and are slightly resistant to moving towards this 'coping' mental space. But it isn't true that doing this will mean you have become 'thick skinned' or changed as a person. Personality isn't something that ever changes as it is the core of who we are and our identity. But we do learn to adapt to our environments and we might build resilience, but that never is a negative thing in life. Increased resilience is something is associated with lots of positive things psychologically including optimism, hope, and high performance (in the workplace, but is is totally transferable here). And actually building resilience is associated with having good social networks which in turn helps us to wear our hearts on our sleeves! So a good thing all round really!