Why are alpine river water green - blue?
According to the website Putting the Emerald in Emerald Lake – Where do the colours come from?, the reason for the colour is the same that occurs in lakes, it is due to what is known as or similar material to 'rock flour' - consisting of


  of fine-grained, silt-sized particles of rock, generated by mechanical grinding of bedrock


and relevant to a river environment


  When the sediments enter a river, they turn the river's colour grey, light brown, iridescent blue-green, or milky white.


The colour is due to:


  the suspended material distorts the wavelengths of light, reflecting back more of the green and blue end of the spectrum 


These usually originate from glacial melt, even though there are no glaciers in the Julian Alps presently, but there used to be, resulting in according to the WP6 Hydro-geological upgrade and improvement of the GIS of the sources of drinking water webpage as having


  The intergranular aquifer in the alluvium of the Soča/Isonzo River, which is composed of fluvial and fluvioglacial gravel and sand sediments with individual lenses of conglomerates


further explained in the article Bovec basin (Upper Soča valley, Slovenia), as having


  Quaternary 
  sediments are represented from bottom to top by partly lithified glaciofluvial sediments, overlain by lacustrine 
  chalk. During the Holocene, the chalk was partly eroded (in some areas totally) and covered by glaciofluvial 
  sand and gravel which are weakly cemented in some parts into conglomerate and by unconsolidated moraine 
  (till).


Potentially, plenty of source material. The particles are small enough to be suspended in the water of the Soča River.