Does power delivery over ethernet always have to use isolated DC/DC converters?
If you want to call it PoE, you need to stick to  IEEE 802.3af-2003 or IEEE 802.3at-2009. 

These standards call for isolation. This answer could end here: no, you cannot build a PoE device without isolation.


  This is also assuming that the data lines are already isolated, so the only potentials without isolation is the power lines.


You also will have a shield in your ethernet cable. On which end are you going to isolate that? Both? Not much of a sensible shield then.

Also, when doing ethernet, you need the magnetics (==transformers), anyway, so get one with center taps on the cable side – no extra effort, basically every ethernet transformer does, anyway. So, without a DC/DC converter that isolates the regulated voltage from the voltage on the line, you'd tie your device's data logic to a fluctuating, noisy voltage that's not guaranteed to be at any fixed relation to the data signals. 

So, really, don't.