Years with clashing trends, aesthetics, pop culture, etc

1993.
Looks and feels 90s, and yet you have songs like these topping the charts that could easily been released in the late 80s:

1981-1984: 80s culture clashing with 70s holdovers
1988-1990: 80s and 90s culture clashing
1996 (some of 94 and 95): Pure 90s culture clashing with early signs of late 90s and Y2K culture
2004 (some of 03): Early 2000s culture clashing with what would later develop or be labeled as mid 2000s
2008: Newer 2000s culture clashing with 2000s culture which was still the norm

I don't feel we've had any major clashes since 2008. Maybe 2009-10 and 2013 a bit. 

1980-1981: Clashes with upcoming early 80s elements and also lingering late 70s leftovers

2000-2001: Y2K trends clashing with early 2000s.

Def agree with 2008-09. You had people with hipster style and into indie rock and being PC and you had people still in 2006.

For the former, I'd say that fits 2002 better than 2001. 2001 I would say McBling wasn't prominent yet, and Y2K aesthetics were still everywhere. 2002 is when Y2K began to decline, and bling aesthetics really started popping off.
2004 seemed to mostly just be emo from my experience. Even American Idiot released that year was a rather dark and serious album. I generally think of that album, Simple Plan, MCR, and Avril Lavigne's Under My Skin when I think of that year, so definitely more emo than "skater pop punk". I'd say that fits 2003 better, since you had darker pop punk getting big, but you also had goofier stuff as well. Think Good Charlotte's The Anthem being big at the same time as Down by Blink-182.

I'd say 1981 is really 80s culture clashing with 70s holdovers. 1982 had a couple but not a lot, 1983 is the first core 80s year, maybe small 70s influence but not substantial, and 1984, like, fuck, that year is PEAK 80s.
1990 being 80s and 90s culture clashing is fucking spot-on. It was a year where shows like Cheers and The Cosby Show were simultaneously on whilst The Simpsons and Fresh Prince of Bel-Air were on + the rise of hip-hop whilst glam metal was still big.
Though you can absolutely make a case for 1991. In fact, I will: that year, the NES was still big, but 16-bit systems like the Genesis and SNES were blowing up. You still had cheesy toy-based cartoons like in the 80s being popular, but you also had shows like The Simpsons, Rugrats, and Ren and Stimpy by that point. Even politically it feels mixed since the Soviet Union fell that year, but Bush Sr was still president. Glam metal's last big year, and grunge beginning its takeover.
I think 1991 was ABSOULTELY a clashing year in terms of aesthetics and pop culture. Fuck, you still had the stereotypical 80s aesthetic being common, but 90s aesthetics were also taking form.