Safe way to dye red patterns that wont run, or turn pink?

[Folklore]

Wife and I are doing cosplays for a con doing cryptids so its our first fursuits. Shes a jackalope im a kitsune.

The question is how to dye red patterns that actually look red and not pink and that wont run that are safe?

We're using synthetics. Acrylic yarn to brush for the tails and acrylic faux fur for the masks. Ive got black and red patterns to make on the face and tail. Looking for suggestions because dyed areas will be touched or brushed after and Im trying to insure no streaking, pink fades or color running or staining others happens. Id hate to pink up a mothmans cosplay with stains or a fresno nightcrawler cosplayer cause I didnt do a good job.

 

[Kellan Meig'h]

For the faux fur, just sew in inserts of the correct color. I.E. if a black spot belongs there, cut a hole in the base fur and sew in a corresponding piece of black fur.