GG, a way to approach it might be something like this. Via email or text or whatever.
Dear mum and dad, I realise you were shocked to find out my current job. Sex work carries a lot of unfair stigma in this country and there are a lot of negative stereotypes portrayed in the media.
I work independently for myself. I do not have a "pimp" and I do not work in a brothel or on the streets. I have me own apartment/work from hotels/whatever. I choose who I see as a customer. I have quite strict screening processes and have a number of security protocols which keep me safe.
The men I see range from young to old, and could be working class guys or top executive types. All of them are polite and respectful - if not they don't get to see me. Many are single and lack the confidence to approach women for dates. Many are very busy with their high powered career and don't have the time or energy for a girlfriend, but feel the need for female company once in a while. Some are widowers. There is no "type" of man who pays for sex.
I enjoy my job and I am proud that I deliver a good service that makes a real difference in people's lives. One client said to me "Thank you for seeing me as a human being and not just a collection of symptoms." [insert your own quote here, obviously] I know that I am making people's lives better.
I understand that you may be feeling shock and experiencing anxiety about my profession. I'll be happy to answer any questions you have. I do not want this issue to cause a rift between us, because I love you so much. I hope we can talk soon."
Hope this might help. Obviously adapt to your own style!