These containers can be either plastic or glass. With few exceptions, neither are recyclable. The kind of thick, heavy-duty glass used for high-end moisturisers is not recyclable glass. Likewise, a lot of makeup products use non-recyclable plastic (usually #6 or #7).
The exception to this is that some companies may use PET or HDPE plastic pump bottles for moisturisers… but these are typically not possible to clean properly. Oily containers with residual product are not suitable for recycling.
What about the makeup itself?
Due to hygiene concerns, used makeup should be thrown away.
In late 2022 Casket Fairprice held a drive for used cosmetics but this is unusual. We don't know if this will be an annual thing.