Thanks wmaiouiru, that's a good point. All three NDVI images use a different color map. I don't know what the Python code image uses for a color map, but that method is more or less deprecated, and I assume few people use it. The infragram.org result above uses a different color map than the Fiji result, but infragram.org does allow you to use a color map very similar to the one used in the Fiji result. At infragram.org/sandbox/, you must chose "Fastie colormap" under "3. COLOR." The other difference between the Fiji result and the infragram.org result is that the Fiji plugin allows you to "stretch the histograms" of the VIS and/or NIR channels. This somehow magically makes the NDVI results much more "realistic." It is not possible to do this trick at infragram.org.
So if the infragram.org result has the Fastie colormap applied (and is reshaped to its original aspect ratio), and the Fiji result does not have the histogram stretch applied, the results look like this:
First image is from Fiji with no histogram stretch and the NDVI_VGYRM.lut color map applied. Second image is from infragram.org with the red filter preset, the Fastie colormap, and the aspect ratio restored.
It might be possible to use Infragrammar in the infragram sandbox to simulate a histogram stretch, but I couldn't figure out how to do that. Most of the people who have the facility to write infragrammar expressions might be more likely to just use Fiji (which is free and awesome). I assume the histogram stretch trick is on the list of features to add to infragram.org. However, this trick is just that -- it makes the result look more like real NDVI, but the NDVI values are not necessarily comparable to legacy NDVI or NDVI from other photos or other cameras.
So a more important upgrade to infragram.org might be to add the ability to calibrate the NDVI result using targets in the photographed scene. But the histogram stretch might still be handy for when there are no targets (and finding targets might be an obstacle).