Scott Manley remarked in a video, SpaceX's Latest Crew Mission Is Unlike Any Other:
[Inspiration4 is] billed as the first all civilian space flight – that's the sort of tagline and frankly it's not strictly correct in many many ways – I mean first of all lots of astronauts were civilians in that they had left the armed forces or never even joined the armed forces – but then you might argue that the spacecraft themselves[*] were you know, built by the government and therefore not civilian [...]
And sure enough Wikipedia's List of spaceflight records concurs with the media (as of 08:00, 16 September 2021):
All Civilian Space Flight
In the formal definition of a civilian:
A person following the pursuits of civil life, especially one who is not an active member of the armed forces.
Was there an all-civilian space flight before Inspiration4?
* Re his last point, if speaking of an object, then it's privately vs. government/publicly funded.