You're collateral damage in the web's war against bots :(
Unfortunately, I think the Cloudflare challenges are designed to filter out users similar to your profile... once you stray far enough from the norm, it just looks like a bot / suspicious traffic to them. Statistically there's not enough users like you (privacy-conscious Linux users on nonstandard browsers) for them to really care enough to do anything about it. Site owners don't care either since you're usually like 1-2% of users at most, and typically also the same ones who block ads, etc., so they don't mind blocking you... it's sad, but I don't think there is really anything you can do about it except conform. It's an ongoing arms race and you're caught in the middle.
Unfortunately, I think the Cloudflare challenges are designed to filter out users similar to your profile... once you stray far enough from the norm, it just looks like a bot / suspicious traffic to them. Statistically there's not enough users like you (privacy-conscious Linux users on nonstandard browsers) for them to really care enough to do anything about it. Site owners don't care either since you're usually like 1-2% of users at most, and typically also the same ones who block ads, etc., so they don't mind blocking you... it's sad, but I don't think there is really anything you can do about it except conform. It's an ongoing arms race and you're caught in the middle.