Crosstalk from RX to TX line on the RS-232 side of MAX3232C
I would guess that it could be lack of supply stiffness with the MAX device.
  Are the pump caps 0.1 uF as shown.   

And what cap is on the 3V3 rail and how far away is it from the IC. 

If the power supply is not stiff enough either because the "pump" lacks energy or the source rail is noisy then something like you are seeing could happen. 

Pin 2 and pin 6 (V+/V-) should have some ripple at the pump frequency but no signal frequency noise to speak of.

What supply voltage are you actually using?

What is the drive voltage on the low voltage side?

It may well not matter but the TI data sheet in figure 4 bottom of page 7 shows differing cap values for different supply voltages. 

The Maxim data sheet shows the same values in table 2 at the top of page 12. Maxim say these are minimum capacitor values. TI says that the same values are typical values. 

Note that the spurious output is unipolar - it's not that it's low - the scope ground is at half waveform height and the proper signal is ~+/- 5V, as it should be, but in spurious mode it's -5/0V. This implies that the + side pump isn't working or that Murphy has proclaimed a bank holiday. I'd start by checking voltages on C3 &amp; C4, supply capacitor size and correct capacitor values.