I used a pareve glass mug for a hot milchig drink and then washed it with a fleishig sponge.
Must I throw out the mug and sponge?
If the water was cold there’s no need to discard the mug or the sponge.
If the water was hot the mug is fine, because we can assume that there was no actual meat on the sponge (unless you know otherwise), and that the soap generally used on the sponge ensured that any taste was “pagum”. However, it is best to discard the sponge.