In my DIY recipes/ingredients to try video, I said that milk can be an acceptable base for DIY masks, if tolerated, but a lot of people have asked if yogurt is also safe. They aren't really all that different, which is why I didn't differentiate in the video.
Yes, yogurt has probiotics, but if we're being honest here, there really isn't any scientific proof that topically applied dairy products--probiotic or not--have any benefits for the skin. There are theories, but nothing definitive. Dairy products containing a good amount of fat can have an emollient (softening) effect on the skin, which is why I think people enjoy them. There is also some lactic acid, but there isn't really proof that there's any really strong action of the components of milk products.
There is, however, some evidence that dairy products applied externally may exacerbate inflamed acne, so I don't recommend the use of milk or yogurt if you are experiencing active, inflamed acne. I also believe that people are far less tolerant of dairy products than we generally think, so if you can use an alternative for a mask base, like unsweetened almond milk, I recommend that instead.
If you are going to use milk or yogurt in a DIY treatment, please only use plain, unsweetened yogurt and milk. There is no reason to be putting sugar, let alone strawberry jam, on your face!