I don’t think The Matrix itself changed much, but it was coincident with and an exemplar of many large alterations that occurred in society at that time (and that many people still insist did not occur, strangely). The internet was picking up its pace of adoption in normies’ lives; online forums and social networks were really starting to attract regular people for the first time. (Yes, Gen Zers, there were indeed social networks well before Facebook. LiveJournal launched in 1999. Also, chat apps and forums functioned as social networks long before this.)
For the first time regular people realized (even if they didn’t conceptualize it in such integral terms) that they were surrounded by the skein of an informational environment that underlaid everything they did and were, that defined them and constrained them with avatars of data that were often considered more real, more meaningful, than they themselves were.
The Matrix refracted that realization through art and artifice; that’s why it hit so hard at the time. And because it wasn’t didactic about it, it had all the more effect. It felt true because it, like a religious experience, injected the mind with something false but revelatory.
People like Ian Welsh for some harebrained reason insist that the internet changes nothing. The reality, though, is that the internet changed everything and The Matrix was one of the first real attempts to artistically grapple with the consequences of this tectonic shift which we were all experiencing and are still undergoing.