I wouldn't throw them out. I'd put them in a box or basket that has a lid or could be hidden easily, then store them under the bed or couch or wherever I could find out of sight and use them up. Combine as many bottles of shampoo together as possible, same with conditioner, etc. Likely would reduce the amount of bottles right there and honestly who cares if one brand is mixed up with another? Reduce their footprint, then use them up.
In the case of makeup, I'd remember that if you haven't used it in well over a year, it likely should be tossed anyway due to hygiene, but shampoo or hair products? You'll save money in the long run by just stashing it and using it up. And going forward, if you find you took a year to use up the hair gel or something? Maybe you don't really need to buy any at all in the future.
Being a minimalist should be about making do with less, which should also mean reducing the amount of things you buy, and not being wasteful. Items that can be used up... should be.
