I found at least one post implying that this would work, but it doesn't seem to for me:

If I go to my inventory and apply filters (i.e. only show mythic rares and rares) and then go to View->Export, the spreadsheet includes entries that do not match nor that show up in the filtered list on the website. I don't think the export needs to maintain sort orders but filters seems like a reasonable thing to do.

Just wanted to add my support here. It would be very useful to be able to export my inventory with the filters applied.

(Sorry, I don't know the policy on this forum about bringing up "old" posts. Hopefully it's OK!)