This is just a lie Facebook wants you to feel. Your sister and mom care about you, they will easily prioritize their family member over specific apps.
You realize that I am speaking from experience not hypothetically; I don't have Facebook and there's been a marked decrease in both the number and frequency of messages from my family who rely on it.
I really wish this wasn't the case. The vendor lock-in with Facebook is really significant and I think those of us who leave the platform have to acknowledge that.
Speaking as someone who never had Facebook, I’ve experienced zero loss of connection with anyone in many networks of family, friends, colleagues, etc. Just a simple email thread to share stories and photos here or there, phone calls, SMS text chats or other apps. It’s so easy and seamless to stay in touch with no part of it involving Facebook.