Protect against large current spikes while not reducing consistent current input

You say the current flowing into the input is 5.5 uA. The voltage is around 1.5, I think, based on a 1.8V drop across T2 (3.3-1.8=1.5). So that means the input resistance is 1.5 / 5.5 uA = 272 k. It is possible that the input does not behave like a resistance, but more like a current sink. In any event, in the specific conditions above, it makes no difference.

So, in effect, the 10k lower leg is transformed from 10k to 10k in parallel with 272k, which is 9.65k. This changes the input voltage by around 30 mV. It doesn't seem to me that this could fully explain the difference you see between your two inputs (1.57 vs 1.5), but to be sure, you should put a 1k on BOTH inputs at the same time. Maybe the two inputs have different resistances or leakage currents.

I think you should entertain the possibility that the circuit basically works, with a small error due to current into the XBee, and the differences you are seeing are actually caused by differences in thermistor temperature. Could you please work out the implied temperature at 1.31, 1.5 and 1.57V using thermistor properties?

Also, I would like to caution you against comparing the 1.31 V reading obtained before connecting the XBee with the 1.5 and 1.57 V readings obtained after. Readings obtained at different times really can't be compared unless you have very good measuring equipment to record actual thermistor temperature and verify that it is the same at both times. Or, if you have the voltmeter connected and you can sit there and connect/disconnect the XBee and watch the voltage jump up and down by 200 mV. That would also be very convincing that the 200 mV is due to XBee. But if you measure 1.31, then de-power the circuit, mess around with it, and measure again and find it is 1.5, well, I would not draw any conclusions from that. Maybe the NTC just warmed up a little due to handling (which is not uncommon). The calculations I asked for will tell us whether that explanation is plausible.

In my toolbox I don't have a negative voltage rail, so I'm planning on using an op-amp to invert my positive rail into a negative and use it to rail other devices.

No, no, no this won't work. An op-amp produces an output voltage that is limited to values within the range of it's own power rails. If you wanted to generate -5V by using an inverting amplifier, the op-amp would need a negative rail of between 5.1 volts and 8 volts.

You can't expect an op-amp to simply generate negative voltages like that.