Just like at home, if you turn on everything in your RV at once you will trip your main breaker. This is called demand factor, you are allowed to hang more loads on a service panel than the panel can handle if they are all on at once. Its still safe because the main breaker will trip. 

If you run both the oven and the air conditioner simultaneously you will be approaching but should not be over 30A. But you most likely have other electrical loads going too. If your water heater and/ or fridge are running on AC and/or your converter is recharging a discharged battery then that could easily put you over. 

So, you could simply be running into a situation where you are running around 30A total load and the 30A breaker at the pedestal is a bit faster to trip that the 30A breaker in the rPod. Breakers are not identical.  One simple check is to see how hot your cord is getting. If its getting hot to the touch, turn some stuff off. Use propane for water heating and refrigeration or wait till you're done with the oven to heat the water. 

What you don't want to do is just bypass a circuit breaker that is tripping (by using the adapter or some other way) and call it good. It could be a weak breaker, but it could also be a real problem somewhere that needs to be corrected before it gets worse and starts a fire. 

One thing to check is which Code cycle the specific local jurisdiction is using. A Code revision is released every 3 years, and the most recent happens to be 2020. But, almost no one will be on 2020 yet. So, I looked back at the previous versions and found that the change requiring edit 30A  20A receptacles whenever there are 50A receptacles present occurred in the 2014 revision. Before that parks were allowed to put in stand alone 50A service, but not anymore. I doubt that there are very many jurisdictions still on the 2011 Code but I suppose its possible. 

The number of sites at an RV park which are required to have 50A service is going up over time, and is at 40% in new parks in the 2020 code.  So, your park owner is partially right in that the industry is moving toward more and more 50A receptacles, but wrong that that will lead to less 30A receptacles being available. 

Just as a reminder, the park owner is not required to upgrade his electrical system to the new standards every time a new Code revision comes out, any more than you are at home. But if he does any new work on his system, including adding 50A receptacles, he is required to pull a permit and assure that all the new work meets the then-current Code requirements. 

So, your park owner can leave what he has now alone, but if he wants to increase the number of sites with 50A, all of the new ones will also need to have 30A receptacles. So, over time, pedestals with only 50A will disappear, which is the intent of the Code writers.