Rinsing/Replacing AC biomedia

[Goes to 11!]

If you clean the sponge right under tap water, yes you will kill BB

Yes, & I do it regularly [As does Hobbs as she mentioned] and it makes no difference whatsoever. - See below.

I don't want to change the topic here but if you clean the sponge under hard-flowing water right from your tap would it kill some of the BB on your sponge? No, It kills all of it.
Should you only do this when you have another filter running so you don't lose BB or is it fine to do whenever?

You should do this when the sponges are dirty. It will make no difference to your bio filtration capacity provided you have colonized biomedia. [Yes the sponge can build up some BB but it's not it's main function and it needs to have good flow]

The sponge is the mechanical filter in an AC - the biomax is the BIOfiltration and is the primary residence of the BB. They don't perform the same function..

Having a free flowing sponge is important and swishing them around doesn't effectively clean them nor does cleaning your sponges affect your BB colony in your Biomedia.