Oh gosh, cookies can be such a pain, can't they? The semi-good news is that the only full site browser that is affected by cookies is Internet Explorer and it's because IE is set up differently than Firefox, Chrome, and Safari. So, if your clients are booking with you on Firefox, Chrome, or Safari cookies will not affect them at all and they will be able to schedule with ease. However, what we have found is Internet Explorer is a little different.
We've also found that folks using the Safari on their iPhones or iPads can sometimes get a cookies error message if they have their cookies marked to "always block" in their settings.
Cookies are required to book on most sites like Facebook, Amazon, Etsy, Ebay...etc etc. However, sites like these and Schedulicity are now moving away from using cookies and instead storing things using the client's local storage. This is why it isn't a problem on Firefox, Safari, and Chrome. Where as on IE or Safari on iOS, if you block all cookies it will disable local storage so then this makes our site unusable.
We moved away from cookies and are using the users' local storage to help them log in with ease, so when you choose the "remember me" that is how that has the capacity to remember you!
So it seems likely that the client(s) that reported that they got the cookie message are using IE to book their appointments and do need to enable their local storage on the browser level. This will allow them to book using the site.
I am sure sorry for the trouble or confusion this has caused not only your clients but you as well. If your clients are having difficulties accessing Schedulicity, we would be very happy to offer our free customer support to them to investigate this further. Our support email is firstname.lastname@example.org!