I can understand not wanting old wrecks that may be a problem but this "We are better than you" attitude really annoys me.
Why assume this is the reason for a photo request. The original poster said they were trying to make a reservation for a month. In many states, once a rental is made for a month or more, evicting becomes a very difficult process, so vetting becomes extremely important. While an older, worn out vehicle may not be an indication that the owners are "lesser", it may be an indication that they are living on a financial edge that could make collecting rent problematic.
DW and I own rental houses, both short term rentals and long term. One of the things we look at when interviewing prospective renters is the condition of their vehicle. Older (or newer), poorly maintained, dirty vehicles full of trash do not make us feel warm and fuzzy about prospective tenants. Most of the properties are now handled by a management company, but I guarantee you that those few properties I still handle personally are not rented to someone driving "wrecks on wheels". Appearance is not everything. It is, many times though, all we have to base a judgement on.
Could this request for a photo not just be a park's attempt to ensure their business attracts clientele that fits the market they wish to serve, and avoid some kind of confrontation/inspection process when someone shows up to claim the reservation?