I haven't been involved in the skate scene for a quarter century, but I'm at least vaguely shocked that Adidas has a team. Does any part of skate culture reject "big business" nosing into a rather anti-establishment culture?
The situation is much less clear cut these days. There are the die-hards that will never ever buy those newcoming brands, sure, but Nike and Adidas skateboarding offshoots do embrace the culture and sponsor great talent with a genuine skateboarding spirit like Sean Malto (Nike), Shane O'Neill (Nike), Daewon Song (Adidas) or Chris Chann (Adidas); plus the shoes are objectively good stuff for skating. They certainly have less of an extreme attitude than Ali Boulala and Dustin Dollin, but that never was what skateboarding was about.
I'm a long-time rock climber, and a handful (or two) of years ago, Adidas jumped into that market by purchasing a well-respected shoe maker (Five Ten). They continue to produce shoes under the Five Ten brand, but Adidas also sponsors a bunch of professional climbers.
There is some cultural backlash in climbing, but mostly around the increasing commodification of the sport (which has always been seen as anti-establishment). Even those folks who rue big climbing competitions and big "shows" (the Dawn Wall climb) still wear Five Ten.