feColorMatrix like most filters operates in the linearRGB colour space. If you want an sRGB colour, Try setting color-interpolation-filters="sRGB" as an attribute on the feColorMatrix.
<svg width="100%" xmlns:xlink="http://www.w3.org/1999/xlink"
viewBox="0 0 640 480" height="100%"
xmlns="http://www.w3.org/2000/svg">
<filter id="cm">
<feColorMatrix in="SourceGraphic" type="matrix"
values="0.0157 0 0 0 0
0 0.3059 0 0 0
0 0 0.7765 0 0
0 0 0 1 0 "/>
</filter>
<filter id="cmRGB">
<feColorMatrix color-interpolation-filters="sRGB" in="SourceGraphic" type="matrix"
values="0.0157 0 0 0 0
0 0.3059 0 0 0
0 0 0.7765 0 0
0 0 0 1 0 "/>
</filter>
<rect width="100%" height="50%" fill="white" filter="url(#cm)"/>
<rect y="50%" width="100%" height="100%" fill="white" filter="url(#cmRGB)"/>
</svg>
It sure looks different to me on Firefox.