Is there any way to export an Inkscape file to another vector format while preserving the blur effects? This is the one and only stumbling block I'm coming across when trying to share my file with other users (most of whom use Adobe Illustrator). I'm usually asked to provide a PDF, and the end product just doesn't look as nice without the blurred areas shown correctly.

No you can't, sorry. I don't believe there is any way around it.

It's funny that Adobe championed SVG but didn't even include proper support in Illustrator.