Does peer review often take away a professor's academic freedom?

Academic "freedoms" granted by tenure at one institution do not extend to a second institution or to any other third party such as an academic journal. In the similar way, US "Freedom of Speech" is about an individual and the government and does not extend to protecting speech between third parties.

Tenured professors are not owed a voice on a third party publication to say anything they like. Just as individuals are not owed a voice on social media to say anything they like.

What professors are owed (any within narrow limits) is the ability to voice some opinions without fear that the institution will dismiss them. In the same way people in the US are free to say and voice opinions (within very wide limits) without fear that the government will jail them.

The question seems to indicate or imply that somehow professors in the academic community should be granted additional freedoms beyond those which individuals have. As if once you are granted some arbitrary status as an academic professor you suddenly can achieve independent financial wealth to do whatever your heart desires. That does not sound like a reasonable prospect to me.

Nothing stops a professor from publishing in a paper or publishing individually their own findings without peer review. I understand that the respected journals in the community do require this and they have their own barriers to entry to get published. If the community wanted to change or if in a professor wanted to change they could simply publish outside of those journals. Asking for some external Force that's not part of the community to break the community standards seems a bit unrealistic. The community should change its community standards if that's what it desires or you should have rogue professors that do this and perhaps eventually the community would change if it's deemed worthy.

As for grants there's nothing that stops a professor from getting independent grants from independently wealthy individuals. I don't see a need that just because you're a professor that you can arbitrarily take money from the citizens of your country or state to do your pet project. I understand that wealth redistribution to whatever class of people that you want seems to be the theme of the day but ultimately you are forcing someone to give up their earned money for another purpose. The government does issue grants for things that are deemed of government or public interest. Private wealthy individuals can also provide grants for things that they deem of their interest. I have achieved professorship therefore give me money because I want to research laying on the beach for the next 25 years seems a bit strange.

Freedom is the idea of doing what you want but what you seem to propose is at least monetarily taking from others to provide freedom to another with zero oversight. If you're taking money from other people those other people should definitely have oversight and input into what that money is used for that is only a reasonable proposition. Taxation voting and government grants provides that oversight. A wealthy benefactor which requires a research toward a specific topic for continued grant money again provides that oversight.

I too wish I had ultimate freedom to do whatever I wanted whenever I wanted but that is not the case in any kind of ordered society. Freedom is freedom of opportunity not freedom of achieving arbitrary outcomes. It seems to me that professors do have these freedoms to pursue opportunities but if no one else is interested they should not be able to force interest in it.

It’s not restricting one’s freedom to not fund phlogiston research. And in the age of the internet, what’s peer review? Stapling thoughts up in the town square was never easier than now.