The smoothie with skim milk and fruit turns into a sort of mousse and it is not drinkable. Not liquid. Have tried two or three recipes with same results.
Milk + fruit mixed together will curdle at some point, the more acidic the fruit, the faster.
Only for very mild fruit like bananas the mix will stay stable for hours or even a day in the fridge. Strawberry is somewhat in the middle and citrus fruit will curdle instantly. And while that effect is desirable in other use cases (think paneer, for example), you probably don't want that in a smoothie.
The right choice of fruit can mitigate that effect and full fat milk is a bit more stable than skim (could be the fat globules?). Also storage times should be considered: what was ok at home can have turned into a lumpy mass by the time you want to enjoy it in the office.
If you are not set on using fresh milk, the acidic varieties like yogurt or buttermilk are a more stable substitute, perhaps thinned a bit.
You could skip the milk entirely, many recipes do, and if it's about the protein, add a power or simply eat a protein-rich food with the smoothie - a handful of almonds goes a long way, for example.
If you swap 1% or 2% or whole milk to skim milk, it should not make a big difference.
At best it should make the smoothie more liquid as there is less fat in the milk.
Are you certain the "mousse" part of it, is not simple that there are more bubbles in the smoothie ?
Me think you should rest your smoothie rest a little bit, a couple of minutes, to let all the bubbles subside.