My primary photography project of the last two years has been photographing areas that are no longer included in Bears Ears National Monument. (it's what brought me to this forum and you fine folks - researching the area) I've had some a show in a gallery here in Denver where I spoke with a number of people about what was going on. I post many of the images I've taken and updates on the latest happenings on either my personal or business social media accounts. I donate profits from any print sales of the images from Bears Ears to the Bears Ears Coalition.
I suggest not only that people vote, but people be informed voters. Politicians on both sides will tell you what they think you want to hear at election time, but oftentimes they'll do something different for the other times. But the biggest thing we all can do, and something I make a conscious effort to do: is vote with my wallet. And that includes trying to use as little of the natural resources that prompt corporations to want to tear up these areas. Marketing 101 - bring the demand down, and the prices go down. Bring the prices down and the profits go down. As profits go down, money for lobbying and the desire to expand drilling areas goes down.
Are these enough? Likely not. But I can't control anyone but myself, and at least I'm making a concerted effort - as are you and many on this site.
As
@scoags mentions, some locals want this for their economy. I'd argue many of those people want it because they're misinformed. They believe what they're being told - that resource extraction is the best thing for their economy. I would argue that in the long run, the economic benefits of keeping extractions out of these areas (or making the monuments the same as the original designation again) and promoting tourism would be a much more viable long-term economic boost. Unfortunately, I don't think you can have it both ways because extractions scar and ruin the tourism possibilities. Imagine Valley of the Gods full of oil and gas wells or a uranium mine, and count the cars driving through there.