Nitter is an alternative front-end to Twitter, and very helpfully gives you an RSS feed of any account. Miniflux is a minimal RSS reader. So I just plop the Nitter RSS feeds in to Miniflux and read the local stuff there.
Both of them are installed via YunoHost, which makes it a doddle to set up.
Feed fetching from Nitter fails periodically. But I just have to force refresh it a few times and it sorts itself out.
Get 404s and 429s returned from Nitter via Miniflux fairly frequently. I wonder if that's Nitter actually returning that, or Twitter?
I could add the RSS feeds to Aperture, but I would feel kind of bad adding a feed for every single Twitter user I want, it's more load on the Aperture server.
So I've also installed Miniflux via YunoHost too, interested to give that a pop as an RSS reader.