A 20lb Propane tank can be safely transported in your mini van. It can also be transported unsafely.
Safely: up right, secured, ventilated, kept cool
Unsafely: on its side, not tied down, un-ventilated, allowed to get warm
The key is to keep it secured, upright, cool and ventilated. The problem becomes on a trip camping are you going to stop for potty breaks? if so how do you keep it cool? Those are questions you will need to consider and answer for your personal situation.
Safety is a mater of degrees, nothing is absolutely safe or unsafe. You asses the risks and mitigate those that you can, with specific attention to the most likely.
You travel wearing your seat belt, what happens if that propane bottle is in the van when you have an accident? If you get rear ended is it going to rupture?