While any residual chlorine or chloramine in your tap water can present a danger to the fish, in an established tank rinsing the filter media in tap with either will not kill the bacteria.
Firstly, when there is ammonia around chlormaine doesn't kill the bacteria, it basically puts them to sleep and a bit of ammonia turns them back on. Chlorine is less effective as well. But both need to be present for longer than they will in the filter media.
Next, the amount of chlorine in the media after you rinse it and put it back into the filter is pretty small. As soon as water is running through it any small amount of chlorine would be so diluted as not to matter. And if you are adding dechlor to the tank or there is some residual still there. The chlorine/chloramine would be neutralized almost instantly in the tiny amount it is present.
I knew a major breeder and then importer in Chicago who rarely used dechlor. I would put changing water into holding containers an let it outgas. Chlorine leaves faster than chloramine. And he always rinsed his media in tap.
The bacteria are a lot hardier than most think.
Lee, W.H., Wahman, D.G., Bishop, P.L. and Pressman, J.G., 2011. Free chlorine and monochloramine application to nitrifying biofilm: comparison of biofilm penetration, activity, and viability.
Environmental science & technology,
45(4), pp.1412-1419.
But if one feels safer not using untreated tap water, then use tank water during a water change. Put some in a bucket and rinse the media in it. No fuss, no muss and no tap