I don't like the term 'Natural' beekeeper ... there is so much prejudice (as has been seen above) about this type of classification. But ... there are a lot of successful and thinking beekeepers who are moving (and have moved) towards a type of beekeeping that does not include some of the staples of the 'conventional' beekeeper. I started from the position that I didn't want anything in my hives that was not 'natural'. So, my hives have never been treated for Varroa with any chemicals and they have always been foundationless. Anyone who says this is 'let alone' or 'catch and release' beekeeping is sorely mistaken .. I spend a lot of time and effort monitoring for varroa, I check for disease and I try to avoid my bees swarming with all the usual methods available. So am I a 'natural' beekeeper and am I irresponsible ? Yes and No as far as I am concerned.
There are a wide range of beekeepers, using a wide range of hives and a variety of different methods in their beekeeping. My view is that it is whether or not you THINK about what you are doing that is important. There are bad beekeepers throughout beekeeping ... regardless of how you try to classify them.