There is a wide range of "types" in the REI world, and I am one of them. I've hiked and camped and rock climbed all over Cali and I've done it with some great people who understand that the wild lands need to be maintained and available for all to enjoy, so long as enjoying doesn't mean destroying. Obviously this range includes neurotic kooks who project their fears and insecurities on helpless baby whatevers, just as there are people in the motorsports world(s) ranging from daredevils to gentlemen racers and genius builders to disgusting belligerent hoons. We can find adversaries on any issue in any group but in my experience most people are reasonable and willing to give and take and work things out, especially once they realize they share similar goals. Well, maybe except on the issue of gun control.
I think Bonneville and dry lakes are in a good position to get support from the SoI. Land speed racing has a long and glorious history at Bonneville and the dry lakes. These places are practically international icons of speed. Add to that the respect shown to these places by the LSR community and I'd think the SoI would see the racers and event organizers as the best examples, the ideal examples, of people using and respecting and protecting wild federal lands. I mean, we take care of the place and we clean up after ourselves. That's a strong ethic in the REI-ish community. We'd get tons of respect from them for that alone. Plus, these are not exactly habitats.
I don't think hippies will be a problem here. (Have they ever been?) The hippies have Burning Man so with respect to the SoI they are in the same situation as the racers. Miners, on the other hand...