I know the old rule that when brush painting, you use separate brushes for gray paints because red and blue colors will tend to distort eh grays.

But what about an airbrush? (I have a Paasche internal-mix type, which so far I have used strictly with Model Master Acryl paints.) Would such a problem occur when using red, then letting it dry, and then using a gray color? Maybe it's a silly question but I like being sure of things.

I am not exactly sure what you mean, but.. I clean my airbrush between colours and alway spray light colours first.

All you have to do is spray your airbrush clear with water/airbrush cleaner between colors. You don't need separate airbrushes for different colors.

I have never even heard of that brush rule. As long as you clean your equipment carefully, you shouldnt have any problems with contaminating it. When you are done spraying one color and want to spray another, spray some thinner through it and wipe the cup clean. I personally always strip down and clean my airbrush after every color, but thats just me.

Oh I do that, even if I'm going to use the exact same paint and color again, simply because if I don't the airbrush would end up clogged and unusable the next time around.

Same here. Metallics are an exception for me though. I found out the hard way that you can't get each and every single metallic flake out paint brushes no matter how well you clean them. So it's separate brushes for metallics and regular paints for me.
Airbrushes are a different thing of course. Clean them properly after spraying metallic paints and you shouldn't have to worry about any residue inside the brush.

I spray acetone through me ab every time I use. And, every third use warrants me tearing it down and cleaning it.

I'm assuming that your question and statement about brushes relates to the issue that it's nearly impossible to remove all paint from a brush. I've found that to be true, even cleaning with Lacquer thinner out of frustration. Separate brushes for different shades makes sense, but isn't very practical nor affordable for most of us.

As for air brushes, I run Lacquer Cleaner through my external Paasche between colors to clean out the gun. What I do change is the color cup or jar, as I can't be bothered to clean them while painting. I have 3 of each, so it's not an issue.

For those wondering why I use Lacquer Thinner for cleaning over anything else, the answer is simple. Nothing is as fast nor as efficient in my opinion. The one exception is Pledge which I clean out with Windex with ammonia followed by warm water.