For starters: If LE wants to nab anyone here, whether for prostitution or soliciting, the easiest place to do so is in person. Additionally, to bust someone for prostitution or soliciting (and have it stick), communications alone aren't going to cut it. Unless you're stupid enough to send messages like "does $300 get me FS/BBBJ/DATY/ QWERTY/LGBTQ/XYZ ? With Greek? Preferably a spinner, hopefully underage!!" If you're that stupid then you're a lost cause anyway.
Anyone running an agency in the current environment should certainly stick to state of the art tech/ privacy measures. Still, that will only protect their clients, and maybe their models, to a degree. If LE sets its eyes on you as an agency owner, they can get you if they want. Merely a matter of time.
For the smart independent ladies here, and their clients, this simply isn't a concern. I'm not advertising for anything illegal, and my email correspondence is watn and friendly, but never explicit or sexual. I also don't store or save ANY information on my email account, I don't even save email addresses, and delete all emails from a client after our appointment. I save screening info just until after a first meeting (for safety purposes), but I do so on a secure, low key offshore service. Same with any other information a client wants me to save for future meetings or references, like email addresses.
So someone getting into my email account could find nothing of interest, unless they're constantly monitoring or catch exactly when someone sends an email with any screening info. For that reason, I have a secure screening form on my site, and also offer a discreet, unpublished, secure email address to which a client can send any screening info if they wish.
As a client, unless your name would jump out to a stranger on a list full of names, you really don't need to worry any more than the average joe about the security of your communications. If your name would stick out, then I would definitely avoid using the services of an agency, since they have much larger targets on their back and a much greater (though still fairly low) chance of having their client lists exposed. If you're actually a celebrity/politician/well known then many ladies will work with you to limit your exposure during screening.
Obviously if you're going through a divorce or are worried about a spouse, that's a separate issue. Make your passwords and usernames unguessable. Use a password generator/vault if possible. Use a separate device or browser for any escort browsing or communication, etc etc etc. The newbie board hands out advise on this topic regularly. Even for those worried about a nosy suspicious spouse, or soon-to-be-ex wife with a private detective, encryption/tor/state of the art privacy tech is going to be overkill for all but a tiny tiny minority of folks here.