So run NoScript. Run in private mode. Block their cookies. Block their address in your hosts file. You can use wget, curl, or any other cookieless downloading tools, none of which will expose you reading The Times to Facebook. RSS doesn't even prevent against this; it can be behind a login, it can require cookies or not serve up info, and it can send info to Facebook denoting you viewed article X. All of which is determined by the server it's running on, not the format of data it serves up.
Browsers are unnecessary for RSS or tracking, and it's a very poor match for browsing behaviors anyway.
Because if you're that worried about Facebook tracking your browsing habits, accessing information via RSS will only prevent some tracking. The Like button is damn near everywhere, not just on news sites. The only way to prevent it is to prevent your browsing tools from communicating with Facebook at all, and hope the servers you're accessing aren't doing it behind the scenes. And/or anonymize your connection (TOR), so even that doesn't give them anything.
The point is that paranoia (valid or not) is not a reason to keep a technology alive when that technology does not solve the problem, especially when solutions do exist. If you want a solution, use a solution, not a crippled, bundled-in-your-browser partial solution that only works under certain circumstances / assumptions.
Are you trying to pitch RSS against privacy enhancing technologies such as NoScript, TOR, etc.? The point is rather that more privacy is a neat side effect of RSS, not its primary purpose.
The primary purpose of RSS - aggregation of content -- works very well, irrespective of bad UI decisions which have nothing to do with RSS itself. And when you pull a full text RSS feed, you're probably far away from "Like" buttons and the like while reading content.
RSS is an exchange format, nothing more. Don't conflate it with some historical transmission methods, nor ignore cases where it's behind a paywall, nor embedded tracking images (since nearly any reader will allow images).
Privacy has nothing to do with RSS. Some feeds I subscribe to have JavaScript and Flash - where's the privacy there? Some are behind paywalls - I'm identified by logging in, and even more so by providing payment info to be able to log in.
Thus, by losing RSS, we would lose zero ability to read privately. It's only viewed as being without all the privacy-sniffing bells and whistles because most providers don't do so. RSS can lose all its currently-common privacy attributes while still being RSS. We should be worried about the loss of privacy online, which is rampant, not the loss of RSS (if it does die). And RSS is a particularly bad flagpole to gather around; anyone up in arms about it is much more likely to be up in arms about privacy than the reverse.
Idea being, that if you want to automatically follow updates of a source (to be just like RSS and not manual), you have to "Like" or "Follow" them on Facebook and Twitter respectively, and then they know who's reading, no matter how many no-script and private mode you apply. FB and Twitter on the other hand shares who else you are liking or following so there you go. With RSS they have no such information.
Based on what causal chain? At best, it's an incredible stretch of a slippery slope fallacy.