Here's the explanation. Cow's milk ACUTELY lowers blood levels of uric acid.
If you recall correctly, low blood levels of uric acid are linked with a faster progression in PD. While clinical trials that seek to raise levels of uric acid are ongoing, the way they're doing it (with inosine) is not without risk of serious complication.
Instead of going that route, let's adjust the things we CAN control. Regular, frequent consumption of cow's milk and dairy products is going to put your levels of uric acid in the lower-than-average range.
If you have PD or a related synucleinopathy, it would be SMART to limit your intake of cow's milk and dairy products. Instead, try soy milk (Silk, etc). If you eat lots of ice cream, try non-dairy alternatives like sherbert.
If you've never tried soy milk before, it's a teeny bit sweeter than cow's milk, but otherwise the taste is fairly similar. It is fortified with the same nutrients as cow's milk (calcium, vitamin D, etc) and just like cow's milk, it's a good source of protein. Similarly, in the grocery store, nowadays you'll find a fair number of tasty non-dairy alternatives to ice cream.
Now, I'm not advocating from removing dairy altogether. Feel free to enjoy the occasional macaroni-and-cheese with dinner.
On a final note, it seems that exercise is also something that can significantly increase blood levels of uric acid. This is probably ONE factor that explains why those who exercise regularly have a slower progression of their parkinson's.