I'd be amazed if Air Tanker was able to decline missions tasked to it by Government. At the end of the day, it was created to become and replace the likes of 101 and 216 Squadron - could you imagine a response which says "we're not flying there - there's a war on"? It surely has an obligation to undertake whatever missions the Government of the day may demand of it - whether you, I, the media or anyone else may like the policy in question or not.
I'd have thought that also gives the ability to offer the most straightforward answer for both Jet2 and Air Tanker should the issue come up more widely. Unless someone can enlighten me to the contrary, if Air Tanker is effectively a Government transport department which has been out-sourced, it has a job to do and has no exercise of discretion in the construct of that tasking.