Stealing (picking up a red-text item) is considered a hostile act, and like all the other ones (murder, casting vigors, entering restricted areas), it will cause all potentially hostile NPCs in the area to become hostile.
In addition, more hostile enemies may spawn in the area. This is not always the case, however. Usually aggression towards the police will result in automatons spawning (especially Mosquito aerial machine guns).
The effect is limited to the current area - the size of this area varies somewhat, but in all cases it is always bounded by changing zones, where you're prompted if you're sure you want to leave the area. If you return afterwards, the hostile enemies will still be there.
There is no long-term impact to these - being hostile in one neutral area has no effect on later neutral areas. There is also no story or plot related changes as a result. Elizabeth doesn't care, and the story marches on regardless of your choices.