I just bought an purple dress shirt, but I don’t really have anything else that’s purple. Would I be better served to wash this shirt with reds or blues? Or either? Or just wash it by itself?
You separate reds and blues?
If it is going to bleed, it’s more likely to bleed the red tones. You might try handwashing it first to see if/how much dye bleeds off. Also, cold water is less likely to cause color bleeding than hot.
Wash it separately or by hand the first few times till it stops bleeding.
Then put it in with your coloured load.
My washing machine has a handy 15’ minute cycle for when you only want to wash 1-2 items.
I use Shout Color Catchers with my laundry–they soak up any bleeding dye. Of course, use cold water.
I wash my blacks in detergent without brighteners. And wash whites separately if I’m going to bleach. Otherwise, no need to sort.
There are ways to sort laundry other than “Jeans and T-shirts” and “Not Jeans and T-shirts?”
Definitely Color Catchers. They are amazing.
“Purples are red, violets are blue.” So if it’s really purple, wash it with the reds. If it is actually violet, wash it with the blues.
I have a similar problem, which is unsolvable. It is a black and white striped shirt that commands me to “wash with like colors.” Like the black stripes? Or like the white stripes? Did whoever put that tag on there actually LOOK at the shirt? Must I go out and buy a lot more black-and-white clothing (not necessarily striped) so I have at least a small load of “like colors”?
If I were faced with the purple-shirt problem, I’d wash it with blacks. As far as the striped shirt goes, I think you’re stuck washing it with darker colors or risk the black stripe bleeding into the rest of your white wash load.
I only do two loads, so one is colored clothes and the other is white clothes. Some of the stuff has a label saying, “wash dark colors separately” but there’s usually not enough of it to matter.
And also, I can’t remember the last time any of my clothes bled. Modern dyes seem really stable.
Striped clothes generally don’t bleed otherwise they would ruin their own white stripes whenever they were first washed. I have never had a problem just putting them in with the white loads. Then again, I haven’t had a problem with anything bleeding in the last few decades. You can usually put everything in the same load and you won’t know the difference especially if none of it is brand new.
Put it in with the whites on a hot wash!
Then everything will be mauve and you won’t have to worry about your whites going grey ever again. 
You wash it with other black-and-white striped garments.
Or you wash the white stripes with your white garments and the black stripes with your black garments.
This reminds me of the story in which a big game hunter makes multiple safaris to Africa, in each of which, he encounters Tarzan busily painting white stripes on a black zebra, or black stripes on a white zebra, or maybe he was painting black and white strips on a blank zebra.