I heard somewhere that it is bad for the air conditioner to be on when turning on the car and that one should turn it off before starting it. Is this true?
It doesn’t matter. The car couldn’t care less whether the air conditioning is off or on. It will not attempt to run the air conditioning until the engine is running, anyway.
I have an old habit of having everything off before I start a car - which means that I basically shut everything down before I turn it off. Its just something my dad taught me to do & it did become a habit. I doubt it does much of importance, but its not as if it represents some large burden & it makes me feel good.
It shouldn’t matter in late model vehicles cause it has the delay A/C start, but like cigroller I have the same old fasion habit I learned from my dad to turn everything off even the radio 
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As I understand it, the problem is not automotive but respiratory !
The idea is that since your AC removes moisture - Humidity from the air and some of it pools within the system, when it sits for an extended period of time bacteria can collect and grow in the pool.
Then, when the car is started the next day the system blows the bacteria into the cabin and it’s occupants inhale it, ever heard of Legionnaire’s Disease ? - same thing.
Either way AC on or off, everyone should roll the windows down before turning on the AC and let the cabin air out for 15 to 30 seconds while the AC is initially turned on.
Its a good idea to start your car with everything turned off - that way you can hear the engine start and run - hear any clunk clunks or screechy screechies.
Um, when you turn the key to the start position, all accessories are shut down in that key position. Turning everything off does nothing because they are already off. To tell the truth I can’t remember if that’s how it was in 1958 but is now.
On all modern cars, when you start the car, all of the accessories, including the air conditioner, have the power automatically shut off. I make it a habit to turn off all the accessories, but I don’t really have to.
Well, they don’t have to be modern, It’s been that way for 40 years or longer.
Someone one this forum once suggested turning off the AC before completing one’s drive to allow the condensation to dissipate before shutting the car down. They suggested that it reduces the likeliood of that musty smell. I don;t really know if it works, but I know it can’t hurt anything, so I’ve taken to shutting mine down.
Either way AC on or off, everyone should roll the windows down before turning on the AC and let the cabin air out for 15 to 30 seconds while the AC is initially turned on.
Better to follow what TSM said in the post above mine. It’s not that you’ll get sick off of any buildup in the vents, but condensation will happen there, and you can get an unpleasant musty smell. Going to vent allows the plumbing to get close to ambient temperature before you turn off the air that’s removing moisture, which makes for less (if any) moisture buildup.