Hello brigid247,
Thank you for using Apple Support Communities. Allow us to share some information with you. According to this resource here: Change your Apple ID photo on iCloud.com - Apple Support
It states the following information:
Your Apple ID photo appears on your iCloud.com homepage and in Settings (on your iPhone, iPad, or iPod touch) or System Settings or System Preferences (on your Mac). If you’re part of a Family Sharing group, others in the family can see your Apple ID photo in their list of family members.
According to this resource, if they update their profile picture via their Settings menu, it will update for family members to see as well.
We hope this information is useful. Thank you for using Apple Support Communities. Take care.