Out of curiosity, can I replace the electrolytic capacitors in the circuit with non-polar ceramic capacitors? Will I get the shifting in level?
MAX232 datasheet: LINK
In short, the answer is yes.
If you look through the DATASHEET, you can see that it is fine to use ceramic capacitors. If you go to page 10, and look at the 'Typical Applications', you will find some notes at the bottom.
In case that wasn't clear enough, it is also stated in 10.2.2, that ceramic capacitors can be used. In fact, you will probably find that the majority of ICs these days can use ceramic capacitors.
This is why it is important to read datasheets thoroughly. The information should all be in there if it is read.