I color my hair red too, and sometimes red/brown. What I have personally found is that many of the "color-safe" shampoos in stores and salons work only marginally better than regular shampoo. Most of them contain sulfates and silicones.

If you CG and cowash, I don't think you'll have a problem, and the color should remain longer, although with red, it'll still fade quicker, unfortunately. If you low-poo, your color will also remain longer. I can attest to that myself. I don't cowash, I just wash less often with a non sulfate shampoo. Since I have been doing that, the red tones in my hair will last about a month.

I agree with the others about the demi-permanent. It doesn't last as long as permanent. A salon I used to go to always used demi-permanent and I didn't realize it; they never told me. It would bleed out within a matter of days. So frustrating! Red is so nice and is such a pain at the same time.
Curltype:Fine, 2C underneath, Mostly 3A, with some 3B thrown in there. Normal porosity.
Shampoo: Elucence, clarify with sulfates 1x per month
Conditioner: Elucence MBC,
Products: Devacurl Angel, LALSG
I can't go totally CG as it weighs my hair down FAST. Hard water.
Bad haircut finally starting to grow out and look normal again!