Safe? Yes, perfectly. Voltage and current levels will be well within bounds of the CAT5 cable.
A good idea? Yes, if done properly.
The analogue inputs do not have a 1MΩ resistor. They have an input impedance in the order of 100MΩ. That's considerably more, plus it's impedance, not resistance. Yes, it does have a resistive component, but it also contains capacitance.
So, that means that at 5V you get 50nA. That's not "close to zero", unless you are standing a long way away. Closeness is relative to scale. 50nA can be seen as next to nothing, or it can be seen as quite a lot
But yes, in this situation it's hardly anything.
CAT5 has a typical resistance of 0.188Ω/m (according to Wikipedia
), so at 30m that's around 5.64Ω. With 50nA running through it you get a voltage drop of (V=R*I) 282nV. That can't make any real difference to the signal sensitivity, since the LSB resolution of the Arduino is about 5mV...
So the cable itself is OK for carrying the signal. But will the signal remain the same, or will it pick up noise?
Well, that all depends on how you wire it up. As long as you ensure you always couple a ground connection with the analogue signal connection then all should be fine. I would recommend 4 wires per sensor (I haven't read up on this one, so I don't know what it needs, but assuming you have power, ground, and signal), of +5V / GND twisted pair, and Signal / GND twisted pair. For every signal have it's associated twisted partner grounded.
You shouldn't run into any troubles.
A far better solution would be to make it 100% digital though. A really small microcontroller with the sensor to convert the signal into a digital signal, and then transmit that data through the CAT5 will ensure the highest quality of sensing. Something like an ATTiny, or a PIC10 would do admirably.