Agree about dying rabbit fur- unless you're looking for something REAL unusual in a color, buy the ready dyed stuff because the color is set and the pelt remains pliable. One thing that happens when you dye furs in small lots is to get the dye hot enough for the dye to penetrate, it changes the consistency of the backing (skin/pelt) the fur is attached to- this is true with calf (tail and body), deer, elk, moose, rabbit, squirrel... almost anything I've dyed. And with white rabbit or calf (kip), no bleaching is required, but with almost anything else you need to pre-bleach, or at minimum pre soak to start with clean, wet materials that have no natural oils on them.
Not as big of a problem with feathers, as you don't need anywhere near as intense heat to set the colors, and I've dyed a LOT of feathers- mostly grizzly saddles, guinea fowl, mallard flank, turkey wing quills and biots. You can actually do most of these in large mason or mayo jars with your dye heated in a microwave, then allow them to set for an hour or so, remove, dip in a vinegar bath, rinse, allow to air dry and then seal and re-use the dye bath a few times.
I heat the mixed dyes for 2-3 minutes on high (jars are kept about 2/3 full) just watch it so it doesn't boil over... and remove with a dry towel, because the jars will get hot. Add the damp material to the jar, stir it around (I use throwaway chopsticks) and make sure it's all submerged well and let it sit. But a cheap strainer and wrap the handle with duct tape or something so it doesn't get confused with kitchen utensils, and remove the materials to a strainer to drain a bit prior to vinegar bathing them- you can buy a glass pie plate or loaf pan at a thrift store to use for this (and label it too!) let them sit for 5 minutes, back in the strainer and rinse. If the vinegar smell is strong, you can make a solution by dissolving 2Tbsp of baking soda in a quart of warm water and run the materials through that to reduce the odor. Rinse again and then place on a layer of paper towels on top of newspapers to dry (so the ink doesn't transfer).
You need to start with the right dyes
though. It has to be an acid dye, one that is designed for use with natural fibers. I get these at a crafts store near me for $3-4 a bottle and that's enough for a lifetime of material dyeing.
And no problem making the colors I've wanted (olive, golden olive, chartreuse, teal, purple, rust, red, scarlet, cranberry). Just write down the amount of the dye you've added, adjust it (and write that down) and then save a card with the mixture on it and attach a sample feather. Generally, start lighter than you want, then add more dye in equal amounts to intensify the color... and for tiny batches of slightly different colors, you can mix small amounts of your pre-mixed dyes together. If you're having trouble getting the dye to set, you can try using some urea powder
but I've never needed it.
As mentioned about furs, no problem if some of these pelts dry hard, because you're going to trim the fur off anyway, but it's a problem if you want to use the fur in strips on the skin. When I do furs, I heat the dye the same way but I cut the fur in small sections (3x3 or less). If you're doing large batch, you will probably want to do this on a stove top. Be sure the pan you're using is heat proof glass or stainless steel so it doesn't affect your color... same rule about using non-kitchen utensils, buy your own stuff for this- it's cheap enough at thrift stores. After you've dyed and rinsed it, you'll find the skin wants to curl as it dries... you can try stretching it out periodically, but there's not much getting away from this, unless you use a staple gun and staple it down to a board placed under the papers... but then you have to watch for rust.
Make sure stuff is COMPLETELY DRY before you bag it and put it away, otherwise it will get mold/mildew.