Subject asks it all, really. I’m just looking to save some time but don’t want my shirts ending up pink or blue!
I’ve always washed/dried all my colors together, as long as it’s a cold cycle, and I’ve never had any problems.
When I do laundry, I just dump everything together. No problem. But then I don’t own anything white, except a couple of old t-shirts.
Whites are fully integrated with colors under my roof. 
I’ve never had anything bleed. I just wash on cold, new pieces of clothing are washed separately the first few times, and never buy clothing made of bright red fabric.
Well, that’s no way to live.
Bleeding color isn’t the problem that it once was unless you mix something new with deep color with bright whites. Quality clothing that has been washed a few times is almost always color stable and washing it together is usually not a problem. Drying it together is even less of a problem. I separate pure whites I but that is only because I add a little bleach to their wash sometimes.
YMMV but all it takes is a little good sense. Don’t mix that new cheap purple T-shirt that your aunt bought for you on a beach in Mexico with the rest of your clothes until you know it won’t bleed for example.
I’m relieved to hear that nobody is advocating “separate but equal” for whites and coloreds.
[ETA: oops, I see somebody already did that]
I don’t really think you’d get any bleeding from any temperature drying cycle. I’d avoid washing them together in hot water, especially something boldly colored for the first few times.
I still separate them, but frankly, the only things I’ve had fade on me have been towels.
Grey is such an understated style…
I still separate my whites and colours. It’s not that they bleed colour and noticeably stain; it’s just that whites washed with colours take on a greyish hue. I see it with the kid’s socks. The ones I’ve washed are white; the ones their dad has washed are off-white.
Dear Quartz’s next of kin…
I agree that clothes don’t usually bleed in the dryer, but some clothes shed lint and others pick it up easily. So you might want to separate clothes on that basis.
They make a handy dandy little dryer sheet that picks up any random color that dislodges from clothing being dried. If I have any doubts about colorfastness of anything I’m drying, I toss one of those in there.
http://http://www.shoutitout.com/en-us/products/pages/shout-color-catcher.aspx
That seems designed for use during the washer cycle, not the dryer cycle.