I do know people that wash some floss - you have to be careful laying it out to dry so that it doesn't get kinky. Of course, you could just lay it out to damp dry, and then put a thin press cloth over it, and iron. The only time any of my regular stitching pals (local) wash is if it's a piece with either a lot of reds, or a good amount of overdye that they fear is going to need washing at the end. One of my friends washed some dark overdyes specifially to soften the gradation of color. Personally, I don't.
If it's kinky - you can always use thread heaven, which I use anyhow with my overdyes.
I use Anchor as well. FWIW, Weeks dyes on Anchor floss, and I'm pretty sure that NN does as well (or did). At the shop, we wash pieces all the time, and have not had any running problems - as long as they're just floss or yarn. I don't know anyone that washes yarn first. I'd really hesitate to do that - especially if it's any kind of blend. I know that when I knit, I now wash the woolens with Eucalan - which doesn't really get rinsed out, as it's good for the fibers. When we block NP, it's pretty wet to start, and haven't had any problems. I've washed some older pieces - no problems - yet.
You just made me think of one of our very nice customers. She came in, wanted to do something a little different with some Irish saying sampler she was about to start. So, I talked with her, and she decided to do a big section in overdyed green floss. I'm sure I told her to check the tags, that it wasn't colorfast, etc - as we do her framing and she's one of the regulars that washes her stuff before bringing it in. Evidently I wasn't emphatic enough. The shop owner calls me up a day I'm not working - "guess what, ---- finished the sampler, and she WASHED it - the whole thing is full of green dye runs" Followed by our debate on my instructions, customer listening, and us giving her a new piece of fabric....
Ellice