People who are into cryptocurrency in general should be cautious of their privacy and security but this people are literally your family members who are concerned in what you do and want to know if you are making a headway from it.
You can be different than me in privacy, but I only tell people who are my family members, but are people I intend to give them inheritance of my bitcoin. I don't plan to tell anyone else about my Bitcoin investment and my Bitcoin wallet backups or exchange accounts, if they are not people who will inherit my bitcoin if I have an accident, lose my conciousness or pass away after that.
Family members can do bad things against you too, who knows?
It depends on how strong family ties are, and it cannot be generalised because even mothers can be not trustworty in exceptional cases. You know your relatives better, so you should be the only one to decide if a relative deserves trust, the chances of he/she telling it to anyone else, and if it's worth the risk.