Also, England bombed Finland during WW2 and they were both democracies
This is probably the most straight forward exception to the theory. I wouldn't count Pakistan in the 1990s as a liberal democracy (nor did the civilian government really have all that much control over the military). But the UK wouldn't have declared war on Finland if Germany hadn't attacked the Soviet Union (and if the Soviet Union had not invaded Finland in 1939) and iirc did not directly engage Finnish units (they bombed Nazi positions in Finland before the formal declaration of war). It was basically an act to show solidarity with Soviet Union against Nazi Germany, not an actual attempt to engage and destroy Finnish military units.
If we go with Freedom Houses's designation of "free," "partially free," and "not free," I don't think there has ever been a scenario where two or more "free" countries have gone to war with one another, but that's only post-1973