What SVG elements display differently when importing the SVG in AI vs other programs

I have the following issue: an svg file looks as I'd like it to look when opening it in the browser or in inkscape, but looks differently in Illustrator. I have made a reduced version of the file that still has the same issue. Can anyone tell me what is causing it and how to fix it? And maybe guidelines of what approaches to use and avoid so that the file would look the same when importing in Illustrator? Here's the file content and how it looks in the browser and in Illustrator.

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