I disagree. It's YouTube that is denying your first amendment right. You have the right to record the officer, but you have no right nor control over what the officer can do. There is absolutely no law against playing a taylor swift song, as distasteful as it may be. He's not stopping the person filming.
There is explicit, and there is reality, and this just doesn't rise to the level of a constitutional violation.
I think the issue is that people are entitled and intoxicated by their "freedom" and publicity. It is not enough if what people say is consumed it must be mass consumed. The freedom of mass publicity is limited by DMCA takedown.
Sure the video could still be held as legal evidence, but the uproar required to get the attention to get it there will not be possible.
People aren't upset police are doing this because it's infringing on their right to record, it's infringing on their limited ability to hold them accountable.
Which I do think is a bad thing, and YouTube should not have automated systems that can be exploited to violate people's rights, but the intention of YouTube is certainly not to violate rights, and the intention of the officer certainly is to violate rights.