People implicitly trust friends and especially family to be generally good and not misuse their information. Far more than they would trust a random stranger or corporation, regardless of legal systems, terms of service, privacy policy, etc. They are also generally grateful that you're providing a service they can use and can handle issues coming up moreso than from others.
And, of course they would, you've built up years of personal trust and relationships with them, which goes far deeper than anything professional.
Source: I do this. For multiple services. For multiple people. But also, just basic common sense.