I say this as someone who has a couple of farmers in the family.
The reality is that a vast majority of farmers do not support a badger cull - most would prefer to inject their cattle to stop the spread of TB but DEFRA won't allow it. Most don't support fox hunting or even allow hunts across their land. I have seen the destruction a fox can do to lambs and chickens ( and even deer calf ). I have no issue farmers shooting them to defend their livestock. One of the farmers in my family that farmed meat probably shot around six foxes a year and then generally only during lambing season.
A vast majority of farmers supplement their income by using wildlife schemes such as being paid to repair or replant hedgerow - or even leave parts of their farm fallow.
One thing you are correct on though - most townies know eff all about farming and the difficulties ( e.g. you ) but at least Clarkson's farm is highlighting those issues regardless of if you like him or not ( clearly not in your case ).
All of this, spot on