I can sure relate to your concerns about "what if…." And once I dip my toe into that ocean, I find out it is bottomless. What if I walk out my door in the morning and a rabid dog attacks me, or a scary stranger flashes me, or tree falls on me? What if my husband goes on a day hike and disappears, perhaps into a bear's stomach? What if I buy my grandson a snack and he gets food poisoning?
I can either let these concerns spin out of control and take over all my choices, or I can recognize them as over-eager "helpers," thank them for bringing a possible bad decision to my awareness and go on living anyway, or allow them to leach the sweetness and adventure out of living.
If I had your concerns about anonymous photographs, I would want to consider how this camp has used photos of kids up until now. If they are group shots of kids having fun at the camp, see whether you can even recognize any of those playful faces. Probably not. And such photos do help parents, and even kids, decide whether or not to go to that camp this summer. (On the other hand, if they snap a "Camper of the Year" shot to post in their newsletter, that would be uncomfortable for a mom with your concerns.)
I personally would be less likely to choose a "faceless" camp with no evidence of kids having happily used their facilities in the past. So yes, they are probably a profit-making organization, but they are probably not promoting any particular child's image as a vehicle for making more money. It's not like modeling. They more than likely just want to show happy, engaged kids.
The organizers would probably welcome a chat with you about your concerns, too. It would be interesting to hear what they have to say, before refusing all rights to photograph your son. You are almost certainly not the only parent with these worries, and privacy is a genuine issue that too many people don't understand until an unwise facebook post comes back to bite them.
But it is impossible to guard against all potential hazards in life and leave enough room for living. There is plenty of adventure and good clean fun in the broad space between "overprotective" and "careless." I hope you find that space!