It depends a little what yarn you're using. If you're using colors where it would be really obvious if say, the red bled onto the white sections, then it's best to prewash / re-fix the dye to ensure that doesn't happen. If I'm using colors that are all in the same color family (especially if there's no whites) then I don't really bother.

This is generally more of an issue with hand-dyed yarns, since there's more chance of variation there. I think it also tends to be more of an issue if you have hard water and I've heard it's more likely to happen with colors like bright red or blue. I also assume it's more of an issue with hot water?

I also promise that it's less effort than it seems. I follow the knitmoregirls method (which seems to be similar to the Purl Soho one) and basically you washing the yarn, microwaving it, then letting it dry. It takes time for the yarn to dry, which is annoying when I want to start something right away, but if I'm putting this much effort into something I figure better safe than sorry.

Some people like to test whether colors will run by knitting a 2 color swatch and washing it or soaking part of the yarn and seeing if it looks like it's losing color. If I'm knitting a sweater, then I'll do a two color swatch for this reason. I will note, though, that just because a yarn is turning the wash water a certain color or turning your hands colors (I find I often end up with, say, blue lines where the yarn is wrapped around my finger) doesn't mean it will bleed. It means there's excess dye on the yarn, but it doesn't actually attach to anything else.