I'm pretty consistently cg and I color my hair with permanent dye. The only time I use a sulfate poo is right after I color it because I want to be certain to get all the color out. It may be possible to get it out with coco betaine which is in a lot of lo poos, but I freak out at the thought of leaving any of that dye gunk on my head.

It definitely isn't great for your hair. What I do to minimize the bad effect is use a protein treatment a couple of days in advance and a great nourishing moisturizer after. Both of those help a lot.
2/c-3a Coarse hair med. density.
Protein sensitive but can use occasionally
Highly porous. Color over grey.
Best 1st day method: Ice Queen!
Stylers: Mix Curls in a Bottle into everything for shine. Terrible pj
Sometimes try roller sets or use a curling brush - classic glamor.
Every day is a gift