You're right, it should have no relevance.
I hold a professional licence and sometimes use it as such for serious purposes, sometimes I'm just using an aeroplane to get from A to B for work or pleasure, and sometimes I'm just going flying because I enjoy going flying and can afford to.
The purpose of my flight should make no difference, save some very extreme circumstances (police / medical emergency, SAR), which don't apply to me personally, but I suppose potentially could.
Similarly, if I'm driving to see my mother in law, to work, or just because I fancy going for a drive because it's a nice day for it, should make no difference to how I'm treated by other road users, by the police, or by the various agencies that provide the road infrastructure.
At the end of the day I'm allowed to be there, the support I need is being paid for, and I'm entitled to use what's there.
G