Effect of Source and Load Resistances on a Filter
So, it seems to me that if we design a filter transfer function with
  the second method, it will be ok for any source output resistance and
  for any load.


No, it will be susceptible to input voltage source impedance. If that impedance were resistive (for example) you could imagine it adding to the value of resistor R1. This will lower the Q (quality factor) of the circuit and raise the cut-off frequency.

However, because an active device is used, there will be little influence on the filter performance and shape if an output load is connected. Clearly, op-amps can only provide drive levels up to a few tens of mA so the load added should not cause that level of current to flow.

Being more practical and understanding that a lot of op-amps may reduce their open-loop gain with a falling load impedance value, this also has to be taken into account on how that may subtly reshape the filter characteristic.