For iOS folks, I can't recommend NetNewsWire more. I pair NNW on my phone and laptop with Fresh.RSS running on my raspberry pi for most of my news and blog feeds these days.
Let's not participate in the corruption of the word "algorithm" here on HN, too. We wouldn't tolerate people saying "integral" when they mean "derivative", so we shouldn't tolerate this, either. We can afford to abstain from this sort of quick-and-easy but sloppy use of language as a shorthand for generic memetic outrage.
And if you're looking to move off of the Twitter app, NNW has a built-in tool to ingest Twitter timelines and searches (you still need to sign in to use Twitter's API).
I tried using a local-only RSS reader after ditching Feedly, but I found myself missing the ability to easily switch between devices.
I ended up setting up a FreshRSS[0] instance which I've been quite happy with so far. It provides the Google Reader API, which is still supported by a lot of FOSS mobile RSS readers (I picked Readrops[1]).
https://f-droid.org/en/packages/com.nononsenseapps.feeder/ https://play.google.com/store/apps/details?id=com.nononsense...