Chemical contamination is a complex issue.
RO will filter some chemicals, such as salts, but not others such as alcohols. Further, some chemical contaminates can degrade the RO membrane.
Distillation is better way to remove chemicals, however, any chemicals with a lower boiling point than water will boil off first and thus must be discarded before collecting the water. Without test equipment it is difficult to know when the contaminates have stopped boiling off.
Conversely, after the water has boiled off, then you may start getting other chemical contaminates boiling off. Again it is difficult to know when to stop collecting the water.
You could just discard the first and last ten percent of the starting quantity of contaminated water. This would eliminate most of the chemical contaminates. However, if you have very little water to begin with, then loosing 20 percent via this method may not be the best solution.
In a survival situation water is the number one necessity, so one may have to take the risk of unknown chemical contamination rather than die of dehydration.
Your nose can help in determining chemical contamination. If it smells like chemicals then you should avoid it. However, if it doesn't smell like chemicals, it doesn't mean that it isn't contaminated.
Your sense of taste can also help in determining some chemicals. Of course, you run the risk of getting either chemical posioning and/or biological infection just by tasting untreated water (even if you spit it out). You could treat for biological contamination first, then taste it.
As, I said, chemical contamination is a complex issue.
Chemical contaminates are going to be a concern in any populated area.
If available, rainwater is the best source of water--provided you collect it directly.
In high mountain streams, you mostly have to just deal with biological contaminates. This is why backpacking purification systems don't generally treat water for chemical contaminates. It is also why they will probably not be sufficient in an urban situation.