What I find works best for me to get rid of toothpaste stains from clothing is too scrape off as much of the dried toothpaste as possible.
Then pour either some vinegar or rubbing alcohol onto the toothpaste stain and let it sit for 10 to 20 minutes and the take an old toothbrush and scrub the stain with the toothbrush and it should come out.
If not you might need to soak the clothes in some warm water with vinegar and baking soda and then scrub the stain again and then run it through the washing machine in warm water to help lift the stain.
You can also use some resolve carpet cleaner on the toothpaste stain on the clothing to help lift the stain away from the clothes.