I have grown the purple carrots, and every other color too. Yep, turned a batch of chicken noodle soup purple. Still tasted fine, but it was a very unappetizing color. I haven't grown the purple ones since, but if I do, they'll be for salads.
Have you tried the red ones yet? I've grown Nutri-Red, which is supposed to be even more nutritious than the orange ones, and was nervous it would turn my soups red, but thankfully it didn't. They have a good flavor, and don't get huge and woody like the yellow or white carrots do.
I've sown carrots 3 or 4 times this year, because some neighborhood cat keeps digging (and pooping) in my veggie bed. Now that the peppers and tomatoes are in hopefully he'll stay out, since there isn't much open space with loose dirt that resembles a litter box anymore. This year, I'm growing St. Valery, Danver's 126, Muscade, Jaune de Doubs (yellow), and Lunar White.