MOTM

> If you are careful to match the input resistors can't you get
> good common mode rejection with active balancing?

No, you can't.
The circuit is ok for some applications, but there are two problems
(in addition to the lack of isolation that was already mentioned):

(1) The two opamp inputs show quite different behaviour in this
      circuit. One is a low impedance (near zero) summing node,
the other has high impedance (depending on the resistors used).
You have the choice between the opamp seeing different impedance
on both inputs (not optimal for bias currents, and for stray
capacitance, see point 2.) or the input having different impedance
for both branches (very bad - kills common mode suppression).

(2) Capacitance. Even when the circuit is perfectly balanced at
      low frequencies, it is certainly not for 1kHz or 10kHz.
      Stray capacitance is always there, and with different resistance
      on both branches even a symmetrcial layout with equal
      capacitance on both sides will result in different pole locations
      for the two inputs. So the circuit may be ok to suppress 50Hz
     (or 60Hz), bit not higher frequency common mode noise.

JH.