You don't, that's the point.
Since it's a CAPTCHA (I haven't actually checked, I'm going by what you've written, I can't access reddit on my VPN), which I suppose they push to prevent bot scraping of their data so they can sell it themselves, the server checks whether you have completed the challenge it sends you with every request. I don't really know the details, but it should be hard to complete properly by a bot, since it watches a lot of things about how you interact with the browser and based on it decides if you are a bot or not. Which also makes it hard to fake the data, since faking it would be done with a bot, which they are pretty good at detecting.
If you don't send it, the server will refuse to talk to you. There is now way around it, other than paying for and using the Reddit API to access posts.
You can use a browser like Mullvad or LibreWolf, that should limit the number of things they can get about you, and using a VPN would go a long way. But VPNs have been recently banned from reddit (at least mine was), and it probably doesn't matter anyway - Reddit is tracking so much about you in background, that the few more data you send to them will not change much.
Such are the consequences of getting addicted to a large corporate product. Why shouldn't they do it? It's more data to sell, and what are the users going to do about it? Leave?