Project Beauty Share
They accept new and gently used toiletries and beauty products. Follow the link and see their mission, what they accept and how to get the items to them.
Dress for Success
There are numerous chapters for this charity. They work to help people to have the clothes, accessories and tools (makeup included) to look and feel successful. They seem to only take new cosmetics and toiletries, however, I'd encourage you to contact your local chapter directly and ask.
Local Family or Women's Shelters
This is a site that can help you identify women's shelters in your area. You can also Google local homeless shelters, family shelters, or women's shelters to find shelters in your area. They often list items that are needed or you can contact them directly to see if they would like your gently used makeup and toiletries.
Send in your makeup donation. They evaluate it and then offer an estimate. Most of these sites will only take makeup containers that are more than 50 percent full.
Reddit.com - makeup exchange
A well-moderated site where you can post the condition and type of makeup you have and find out whether anyone is interested in it.