Hair conditioner most times has a lot of byproducts that stay in the hair (by design) eg, Castor oil, Alcohol, And various forms of silicones, as well as fragrances. The reason those things stay in hair is to give them shine, smoothness, control, color protection, volume etc. The problem arises when these things build up in the hair because the shampoo being used is not high enough in surfactant levels to wash out conditioner byproducts completely, or even the shampoo itself has lots of byproducts on their own. It's at this time a Clarifying (deep cleansing) shampoo is needed.
Now I know this sound like a lesson a Hairdresser would give a woman, because it is. I am one. And in my line of work I use hundreds of hair products daily. So the thought of using Hair conditioners on a silver tip brush is a bad Idea. I wouldn't want to have byproducts, building up in my brushes so I can load them on my face later. It (hairconditioner) may feel softer and work at first, but belive me it WILL build up on there. Now I know that a good soap will cut and cleanse all of those things from the brush, but then you might be adding extra stress to the integrity of the badger hair itself by using such high surfactant level cleansers.
My advice and input and thoughts would be to never use anything other than facial cleansers to clean out your brushes, and not to ever use hair conditioners. Vineger, boiling water, hand soap are out too. You don't want overuse of these things to permanently damage the badger hair (which doesn't grow back on your brushes). Facial cleansers at most and always air dry. BTW. isn't badger hair soft as a feather anyways? if not the badger hair may have been damaged. Hope this helps someone.
All the best -J