First, strict Jews would avoid places where dairy and meat products can come in contact with each other.
The milkshake formula might have all sorts of crazy stuff in it, so that would be risky at best.
Fries are often cooked in oil flavored with beef tallow, making it a no go. If the same fryer is used for deep fried non-kosher chicken, a double no-go.
The soda is the safest bet. It would be better still if it came in a sealed bottle or can.
Okay, that makes sense. Thank you for the additional information.