A hit to the tail could puncture a fuel tank in the OMS pods, leading to a leak of flammable, toxic fuel. That would probably require an emergency evacuation of the shuttle on landing, assuming it made it to the runway at all. Or it could damage the APU or its fuel system, also located near the tail, leading to a loss of hydraulic pressure for the flight control surfaces. A puncture in the belly of the shuttle could hit the cryogenic oxygen or hydrogen tanks, leading to a fire or explosion there, or a loss of power from one or more of the fuel cells fed by them. Damage to the reentry shielding won’t matter by the time the shuttle is in missile range, since by then it’s already past the dangerous part of reentry, but enough physical damage to the aerodynamic surfaces could create drag or impair controllability enough that the shuttle wouldn’t reach the runway. It’s a glider, and there’s not much room to diverge from the planned flight path before it doesn’t make it. A hit on a landing gear door could damage the tires or jam the gear mechanism, and the shuttle isn’t designed to survive a landing with any gear retracted or wheel-less. And of course, a missile hit on the crew cabin could injure or kill crewmembers or damage the flight control computers.
I suspect that it would be very difficult to hit a landing shuttle with a shoulder-fired missile. For most of its reentry, it’s far too high and going far too fast. IIRC, the approach to the runway is taken steep and fast, so it’ll probably only be in missile range for a very short period of time before landing. You’d have to be in just the right spot, near the runway, to pull it off.