Hi Julia -
I take those serious. Most of my clients have the free accounts, along with their business accounts. One of my clients is in the IT business so all of his tech's can view his emails if wanted. I take care of his personal business and rental houses and we conversate through his gmail account instead of his email through his company. Another client is a financial coach and she uses a hotmail account, for us to communicate and for me to schedule her clients with the hotmail calendar, she says it's easier to use than her domain email. I have one client that also has an on-site assistant, and even though we usually collaborate, there are issues the client likes to discuss privately through a personal email account. Although they all have their own domain and email address through their business.
That's why I take those serious! Hope that helps you some