Since all browsers render it the same way, it would seem likely that this is a bug in the AI SVG export filter.
To me it looks like you are applying a blend mode ("Overlay" perhaps?) to the white parts on top of the image. That effect ought to be reproducible using SVG filters, but perhaps AI's exporter doesn't support that yet.
If you are using an "odd" blend mode, try changing it, or reproducing the effect another way.