How strange. I don't even own indoor slipper--I would think others would be in the same boat.
Is the issue just that they don't want shoes that have been outside to be inside, because they could be dirty? Or is it that they want shoes that will be quiet and won't make any noise (as heels might do)? If you had the time and funds, I think I might go out and buy an inexpensive pair of new flats, and take them, new, to the conference. If they haven't been worn outside before and are flats, it seems like they might be acceptable.
If that's not possible, I guess you have no choice and have to wear your slippers? :( Maybe they wouldn't look as bad if you wore long pants? I guess everyone else will be wearing slippers too, so at least everyone will look silly together.
