When sending text messages to clients, a distinction must first be made between transactional and marketing messages. Appointment reminders are transactional messages, because they are directly related to an order (or appointment). It is therefore your legitimate interest to send these messages in this context and you do not need the explicit consent of your clients.
This document is for informational purposes only and does not constitute legal advice. Remind1 users should always seek legal advice before taking any action with respect to these matters.