You could use FFT in xmtr and IFFT in recvr - nothing will go wrong. You can do IFFT then FFT or FFT then IFFT. Both will give the same result. See **broken link removed** and select Tutorial 22 and look at page 11.
However, you obviously can't do FFT then FFT nor IFFT then IFFT. You have to do one of them (pick one) then the other.
So, if you make a transmitter and I make a receiver, we better know which uses which transform - we can't both use the same one. They are different, but given any input, they both produce the same output. But given that output, if you want the input back, you have to use the 'other' one. So you must do either IFFT then FFT or FFT then IFFT.
My educated guess is that we mostly think in terms of the Fourier Transform as converting signals from the time domain into the frequency domain. The inverse of that would convert from the frequency domain into the time domain. Since we want to transform frequency domain signals in the form of multiple carriers ('subcarriers') into a time domain signal that can be transmitted, then it's logical to think of that process as the inverse Fourier Transform. But it could be done just as well using the ('forward') Fourier Transform. Anyway, to keep everyone (all those who will make transmitters and receivers) on the same page, let's decree that it will be IFFT in the transmitter and FFT in the receiver. Could have been the other way 'round!