Let's ponder the concept of "so you put some plants out in the yard and they get rained on" - it's the same water - so it really should not be any worse.
If you incorporate a standard trick of roof rainwater collection ("roof-washing") - basically letting the first few gallons go, so that any accumulated dust/bird poop on the roof and the initial pollutants removed from the air by the rain are diverted rather than stored, the stored water should be of somewhat better quality than what falls directly from the sky including the initial pollutants. Bird poop is more of a concern for drinking water than irrigation water, of course, but the dust on the roof can be pollutant-derived or have an abnormal pollutant load attached to it.
You can also coat your collection (roof) surface with an acrylic roof coating if you have concerns about the surface itself contributing problematic materials to the water.
With the end of leaded gas, a main concerning airborne/rain-washable pollutant for LA's microenvironment has been largely eliminated.
However, all this is handwaving if you already have stored water, rather than you are contemplating a new system - take a sample and have it tested, particularly for heavy metals (as being one of the more problematic items for uptake and concentration in plants) or the testing lab's "standard suite of tests for [food plant] irrigation water" if they have one.
Acidity, if at a high enough level to be a concern, is easily addressed by tossing a bag of marble or limestone chips into the storage tank, or incorporating a pass through a bed of them on the way to the tank.