If you rinse your media with tap water, you are killing off all your bacteria! (unless you have well water) So don't do that!
Maybe yes, maybe no.
To have such highly chlorinated tap water that would destroy all bacteria with rinsing would be a stretch.
Is it a bad idea to use some tank water to rinse your filters, no.
Is it a “must do“. Also, no.
There is this ongoing myth that a tap water rinse will destroy all your beneficial bacteria and throw your tank back into a cycle.
If your tank has successfully cycled, you have bacteria throughout your system, not just on any filter material.
Any die off, due to tap water cleanings will quickly be replaced as the bacteria grow to process the load.
Again, not a bad idea to use your tank water for “bio bathing”, but no biggie if you “tap” it.