This goes beyond just UX. When I started in this industry in like 2001, I was interested in HTML, magazines, web design, logo design, media. The worst advice I’d consistently get from CDs and managers was to specialize.
More importantly, I can incorporate other wild ideas from completely different interests, like education theory, music, economics, accounting, media criticism, etc. Give yourself over to your inputs and figure out weird ways to channel 'em. That's what being a generalist is.