All-white whites can be easier to wash than fabrics with some color in them, because bleach may not be an option for the latter, and hot water can cause some dyes to bleed.
When washing these items, check the care label to find out whether bleach is a no-no and whether cool or cold water is preferred over warm or hot. If you must turn down the temperature, by all means do so. Otherwise you could end up with a suddenly green shirt with green stripes that would only fit a toddler.
For your bleach-safe, hot-water-safe load, you'll follow the instructions for your pure-white load with the possible addition of a laundry "dye catcher." This additive (either in liquid or sheet form) catches loose dye in your laundry water and keeps it from re-depositing. This product can also help remove dyes that have already bled.
For whites-with-colors that don't like regular bleach and/or hot water, you can switch those out with a color-safe "bleach" (which contains hydrogen-peroxide) and/or cool water and still add the dye catcher. Those articles won't be disinfected, but they should still be acceptably white.
Worse comes to worst, when removing a stain from a mixed-white piece, you might want to think about spot-bleaching with a cotton-tipped swab (and gloves!), applying it only to the white, stained area. Again, though, this is not great for the fabric, so if you take this hail-Mary approach, rinse, rinse, rinse. Bleach residue can wreak havoc.
Finally, a few additional white-washing (and general laundry) tips ...