SilverFox,
I agree with your thoughts... it is probably a build up inside the pipes. The drain pipes are the same used in a Stick Built Home. Black ABS plastic... so the usual drain cleaners should not harm the plumbing of the RV. I have used a drain cleaner in our BigHorn.
Question might be what to use if the RV Park has a Septic system. Although I doubt if the typical drain cleaners would give any serious problems to a septic system.... I have used it when we still lived in Ohio... We had a old septic system... never had a problem.
I feel the different products we often use when taking a shower leads to this build up... hair conditioner is one... a wax type product... it could help coat the pipes as it flows down the drain. We have stopped using "Bar type Soap" but now use liquid soap. I have had issues with both the shower and the bathroom sink drains. The bar type hand and face soap seems to collect inside the drain pipes... when I finally paid attention to what most public buildings (Rest Rooms) use.... it's always a liquid soap. I believe it gives them far less problems over all.
Just my thoughts...