Anything so severe as what is originally posted points to incorrectly configured equipment (crossover, etc). The room and speaker placement certainly plays a large part in any EQ changes you should make, but I generally find that I can leave things flat, except in certain circumstances where room layout and speaker placement result in "boomy" bass. I don't have an RTA, but since I play bass I find the offending notes and cut as appropriate (I carry a chart that shows notes correlated with frequency). I usually don't have to cut a lot, and in only a very small area (just a band or three.)
I agree with an early poster that you should baseline your system in a "clean" room or facing out of a garage, so you know what settings result in your desired sound. Then you should only need to tweak a little bit once you're at your venue.
One caveat to all this. Be sure you're testing at a level similar to what you normally play. Also have the monitors switchable in and out to compare. Some bands crank the monitors so high that they almost don't need FOH sound, which results in difficulty achieving a clean FOH mix. I'm fortunate that (in my band) we all use in-ear monitors and all play through the main P.A. (no separate guitar amps), so we have an easy time getting clean sound. Now if only we could better isolate the drummer...