Given the park service trend towards reservations and lotteries and limitations: good luck with access. I'm certain there is a plan, most likely benefitting the Ahwahnee crowd much more than the Camp 4 club.
This would be a lot of my fear about this proposal. Its been playing out a lot in exactly this manner all over the west for a while now, so its something I'm not looking forward to.
Personally, I do all kinds of outdoor stuff, from mountain biking to hiking and backpacking, to doing the hard 4x4 trails, all in the Shaver Lake area and making that whole area a national monument is going to be a net negative for a lot of outdoor activities in the area.
Given that Biden's term ends in a couple weeks, I doubt there is zero any of us can do at this point to influence whether this is created of not. A bunch of state legislators supported it (edit - I'm uncertain about the Governor's support), the local Chuckchansi tribe opposed it (along with vocal opposition from HOV organizations). There is no way the Trump admin would support this, so if its going to happen it will in the next ~20 days