I'm not 100% sure, but I think hippy's 22K and 180R passes all these tests
Not 100% - The output shorted to 0V would draw 28mA, above official rating for most pins, if shorted to +20V, 111mA, to -20V, 139mA which are both well over. Also a short on an output could drive the port over its rating when adding the current used for other pins. Running the PICAXE other than at 5V will increase / decrease short-circuit currents in fault conditions.
For the Serial Out pin ( at 5V operation ) that 28mA shouldn't be a problem as the output would not be permanently high, just pulsed, and the PICAXE is fairly robust and seems conservatively rated as has been observed. The 180R can probably be increased to 220R or higher if desired.
The interface suggested is used to simplify the circuit and reduce cost, is assumed to be used only when wired correctly, offers reasonable protection against common mistakes ( shorting output to between +V and 0V ) and limited protection against bigger mistakes.
MAX232 and their ilk are designed to be more robust to fault conditions which is one reason they cost more. I have no idea how most MAX232 substitute circuits stand up to fault conditions. You'd have to work that out, ask the designer, or test it - The circuit in Post #1 probably wouldn't stand up to a voltage applied to pin 2, the FET would short that voltage to 0V.