Sounds like you need to decide on your policy and raise it at a staff meeting to ensure everybody fully understands the situation.
In some respects the situation has been taken out of your hands due to new data protection legislation being introduced. That might make it easier for you to raise the issue and point out that it’s the law and not just you being awkward.
Firstly, you need to ensure that clients sign a document allowing the salon to post their image to its social media pages. Secondly, insist that staff only post on the Salon pages and not on any personal pages, otherwise, it will become a disciplinary matter. If the staff do post pictures without seeking permission and a client complains via the legal route, it’s likely that you rather than the staff member who will be prosecuted.
Are you a member of the National Hairdressers Federation?
It’s worth joining in my opinion as they provide excellent guidance on a range of staff issues that you can refer to without having to be an expert in Human Resources.