Sounds silly but wait... Salt would make the toothpaste become an exfoliant, adding a scrubby quality to the paste. it also constains "whiteners" and antibacterial properties, and acne is mostly bacterial. I'd say this has a very good chance of actually working for good and logical reasons.
How to Naturally Remove Makeup: 3 Easy Makeup Remover Options
The makeup remover balm recipe is my absolute favorite (#3). Works so well and leaves my sensitive skin feeling great and makeup- free! Great ideas, using simple ingredients, for how to naturally remove makeup.