In regards to the deodorant price differences, and soap, the cost difference is logical because men go through those products much faster, thus the price is less.
My wife will buy a smaller stick of deodorant than the one I get and when mine is all gone, her stick is still about half.
My bottle of shampoo runs out faster than hers. My soap turns into a sliver hanging halfway down the drain while hers is still a good size.
Now for the record she tidies up as much as I do, and I noticed the same thing in past relationships too.
Thus the price difference is relative to how often a product is bought.
McDonald's is cheaper than some other fast food restaurants because they have more demand. A 24 of Budweiser will be cheaper than a 24 of a beer made from a mom & pop company just getting through the door.
Price is relative to demand, and while there is a great demand for many female products, it is affected by how often those products are replaced (bought again)
Most men generally burn through their products faster than women, thus the demand for those products is slightly more.... Which leads to slightly lower prices.
If women sweat and got as dirty as much as men during the regular working day, they would end up using just as much of those products, thus demand would be similar, leading to lower prices.
As for makeup, I couldn't tell you as I don't wear or buy any.
Shaving cream/gel also applies with gender specific demands. Most men need to shave much more, much thicker hair than women's thinner hair in just the armpits and legs, etc. So again, more demand, lower cost.