Can you slow down the baud rate from the barcode reader? Or is it that the wifi library is disabling the serial input pin's interrupt-on-change altogether?
I have put an oscilloscope in the input pins and the data is present but the Wemos will not acknowledge it.
I have been trying different pins to see if that makes any difference but nothing concrete yet.
The fact that you are receiving nothing, vs receiving corrupted bytes, makes me think that the software serial uses a pin-change interrupt or possibly a periodic timer, and that this is being disabled or blocked for longish periods by wifi interrupts.
I am thinking hard of a workaround, but so far nothing. My next step would be to dump the interrupt config registers before and after starting the wifi and serial interfaces, see if that is indeed the problem. And see if the serial interface works ok for > first packet if wifi is commented out.