Anonymous phone lines. There was (and still are) many services you can call up anonymously for help. If you’re worried about it being traced back to your phone then you’d just go for a walk and use a pay phone.
The internet made it a lot easier though, and lets people get a lot more help from a wider variety of services (and communities).
A lot of things were not recorded, there were no mass video recording, no cell phone location tracking, no ALPR, low credit card use with high cash usage and what was recorded was in the bottom of some basement cabinet of some government office.
Libraries had very strong privacy protections culturally and legally.
If you lived somewhere with good transit and didn't have a papers please id culture, you could also travel without any identifying information on your person!
If you had half decent opsec, the only thing to worry about is people you know noticing you somewhere, and even that is reduced by driving somewhere 1 hour away.
