That's actually not the RSS reader's fault. It's the rss feed you import that behaves like that. It's on purpose, to make you go to their website and ingage in their traffic.
Not a solution for everyone, but I am selfhosting and using FreshRSS. One of the extensions is Readable which will fetch the entry's URL and parse it using either Readability or Postlight Parser to replace the content of the entry and make all of it available in the reader.
In a lot of CMSes that offer RSS feed generation, there's a setting you can frob - either put the entire article in each RSS entry, or just the first X words in the <summary></summary> block. A lot of them default to the latter and folks never turn on the former.
Best way around that I've found is with feedme on android. It's got a mobilizer with a customizable css selector. Just set the app to load the feed in web view and to use the mobilizer and you're good to go.