I had a look at your SVG. When opened in Inkscape 1.0, I can't see any evidence of blending modes, although I can see it when I examine the XML. What version of Inkscape are you using?
SVG blending modes used to be a bit iffy with patchy support in browsers, but modern browsers now seem to support SVG layers with Blending modes. Perhaps consider moving the shape to be blended onto its own layer, then set the blend mode of the layer. I tested this and it seems to work using Inkscape 1.0 and viewing the SVG in Chrome, Firefox, and MS Edge. Here's an example
Obviously this doesn't mean that the SVG will necessarily render properly in other vector image editors which might not support current SVG standards to the same extent as Inkscape or modern web browsers. For example, the SVG I linked to doesn't render properly in Adobe Illustrator 2018. But Illustrator is notorious for its poor SVG support.