Not that early
These weren't THAT early of viruses... UNIX systems after all had already been getting viruses 10 years earlier, and in fact DOS systems had been getting viruses throughout the 1980s too.
And Window (circa late 1990s) lack of security can't be blamed on a 1960's-style lax culture... UNIX (especially BSD UNIX) definitely has a countercultural background to it, and in fact was quite insecure in the 1980s*. Morris worm came out in late 1988, and woke up the UNIX vendors that security is important. The Microsoft and UNIX cultures were just so seperate that, despite the clear warning on what can happen to insecure networked systems, Microsoft decided to totally ignore security until things seperately came to a head on Windows systems.
*flaws in 1980s UNIXes.... just to name 3 off the top of my head... UUCP -- UNIX-to-UNIX CoPY -- typically set up so actually any file off the system, including the password file, could be requested for download; unpassworded guest accounts; some vendors kept a root-level "field service" account on their systems, username: field and password: service.